# Martin Kutrib's research while affiliated with Justus-Liebig-Universität Gießen and other places

**What is this page?**

This page lists the scientific contributions of an author, who either does not have a ResearchGate profile, or has not yet added these contributions to their profile.

It was automatically created by ResearchGate to create a record of this author's body of work. We create such pages to advance our goal of creating and maintaining the most comprehensive scientific repository possible. In doing so, we process publicly available (personal) data relating to the author as a member of the scientific community.

If you're a ResearchGate member, you can follow this page to keep up with this author's work.

If you are this author, and you don't want us to display this page anymore, please let us know.

It was automatically created by ResearchGate to create a record of this author's body of work. We create such pages to advance our goal of creating and maintaining the most comprehensive scientific repository possible. In doing so, we process publicly available (personal) data relating to the author as a member of the scientific community.

If you're a ResearchGate member, you can follow this page to keep up with this author's work.

If you are this author, and you don't want us to display this page anymore, please let us know.

## Publications (299)

Deterministic synchronous systems consisting of two finite automata running in opposite directions on a shared read-only input are studied with respect to their ability to perform reversible computations, which means that the automata are also backward deterministic and, thus, are able to uniquely step the computation back and forth. We study the c...

Input-driven pushdown automata (\(\text {IDPDA}\)) are pushdown automata where the next action on the pushdown store (push, pop, nothing) is solely governed by the input symbol. Here, we introduce sweeping input-driven pushdown automata that process the input in multiple passes (also sweeps). That is, a sweeping input-driven pushdown automaton is a...

Exclusive nondeterministic finite automata (\(\text {XNFA}\)) are nondeterministic finite automata with an exclusive-or-like acceptance condition. An input is accepted if there is exactly one accepting path in its computation tree. If there are none or more than one accepting paths, the input is rejected. It turns out that, from a descriptional com...

We introduce and investigate tree-walking-storage automata, which are finite-state devices equipped with a tree-like storage. The automata are generalized stack automata, where the linear stack storage is replaced by a non-linear tree-like stack. Therefore, tree-walking-storage automata have the ability to explore the interior of the tree storage w...

Top-down syntax analysis can be based on [Formula: see text] grammars. The canonical acceptors for [Formula: see text] languages are deterministic stateless pushdown automata with input lookahead of size [Formula: see text]. We investigate the computational capacity of reversible computations of such automata. A pushdown automaton with lookahead [F...

Deterministic one-way time-bounded multi-counter automata are studied with respect to their ability to perform reversible computations, which means that the automata are also backward deterministic and, thus, are able to uniquely step the computation back and forth. We study the computational capacity of such devices and obtain separation results b...

String assembling systems are biologically inspired mechanisms that generate strings from copies out of finite sets of assembly units. The underlying mechanism is based on piecewise assembly of a double-stranded sequence of symbols, where the upper and lower strand have to match. The generation is additionally controlled by the requirement that the...

An iterated uniform finite-state transducer (IUFST) runs the same length-preserving transduction, starting with a sweep on the input string and then iteratively sweeping on the output of the previous sweep. The IUFST accepts the input string by halting in an accepting state at the end of a sweep. We consider both the deterministic (IUFST) and nonde...

Reversible programming languages have been a focus of research for more than the last decade mostly due to the work of Glück, Yokoyama, Mogensen, and many others. In this paper we report about our recent activities to optimize reversible code with respect to execution time. Based on our rc3-compiler which compiles Janus to reversible static-single-...

An iterated uniform finite-state transducer (IUFST) runs the same length-preserving transduction, starting with a sweep on the input string and then iteratively sweeping on the output of the previous sweep. The IUFST accepts the input string by halting in an accepting state at the end of a sweep. We consider both the deterministic (IUFST) and nonde...

Input-driven pushdown automata (\(\text {IDPDA}\)s) are pushdown automata where the next action on the pushdown store (push, pop, nothing) is solely governed by the input symbol. Nowadays such devices are usually defined such that every push operation pushes exactly one additional symbol on the pushdown store and, in addition, the devices work in r...

We consider parsers of deterministic context-free languages and study the sizes of their syntax checking components. More precisely, we allow the input processing from left to right or, alternatively, from right to left, whatever is best for the given language. We establish an infinite sequence of deterministic context-free languages \(L_k\), for \...

To determine the computational capacity of cellular automata they are often investigated towards their ability to accept formal languages within certain time constraints. In this paper, we take up an opposite position and look at cellular automata towards their ability to generate patterns, within certain time constraints. As an example we describe...

We introduce and study input-driven deterministic and nondeterministic double-head pushdown automata. A double-head pushdown automaton is a slight generalization of an ordinary pushdown automaton working with two input heads that move in opposite directions on the common input tape. In every step one head is moved and the automaton decides on accep...

Iterative arrays whose internal inter-cell communication is quantitatively restricted are investigated. The quantity of communication is measured by counting the number of uses of the links between cells. In particular, iterative arrays are studied where the maximum number of communications per cell occurring in accepting computations is drasticall...

We study the computational capacity of self-verifying iterative arrays ( $${\text {SVIA}}$$ SVIA ). A self-verifying device is a nondeterministic device whose nondeterminism is symmetric in the following sense. Each computation path can give one of the answers yes , no , or do not know . For every input word, at least one computation path must give...

We investigate finite automata whose state graphs are undirected. This means that for any transition from state p to q consuming some letter a from the input there exists a symmetric transition from state q to p consuming a letter a as well. So, the corresponding language families are subregular, and in particular in the deterministic case, subreve...

Partial word finite automata are deterministic finite automata that may have state transitions on a special symbol \(\diamond \) which represents an unknown symbol or a hole in the word. Together with a subset of the input alphabet that gives the symbols which may be substituted for the \(\diamond \), a partial word finite automaton (\(\diamond \te...

Deterministic pushdown transducers are studied with respect to their ability to compute reversible transductions, that is, to transform inputs into outputs in a reversible way. This means that the transducers are also backward deterministic and thus are able to uniquely step the computation back and forth. The families of transductions computed are...

A string assembling system is a generative model that generates strings from copies out of a finite set of assembly units. The underlying mechanism is based on piecewise assembly of a double-stranded sequence of symbols, where the upper and lower strand have to match. So, the generative power of such systems is driven by the power of double-strands...

Top-down syntax analysis can be based on \(\mathrm {LL}(k)\) grammars. The canonical acceptors for \(\mathrm {LL}(k)\) languages are deterministic stateless pushdown automata with input lookahead of size k. We investigate the computational capacity of reversible computations of such automata. A pushdown automaton with lookahead k is said to be reve...

Descriptional complexity has historically been a multidisciplinary area of study, with contributions from automata theory, computational complexity, cryptography, information theory, probability, statistics, pattern recognition, machine learning, computational learning theory, computer vision, neural networks, formal languages and other fields. Som...

Reversible programming languages have been a focus of research for more than the last decade mostly due to the work of Glück, Yokoyama, Mogensen, and many others. In this paper, we report about our recent activities to compile code written in the reversible language Janus to reversible static-single-assignment form RSSA and to three-address-code, b...

While the closure of a language family \(\mathscr {L}\) under certain language operations is the least family of languages which contains all members of \(\mathscr {L}\) and is closed under all of the operations, a kernel of \(\mathscr {L}\) is a maximal family of languages which is a sub-family of \(\mathscr {L}\) and is closed under all of the op...

In contrast to many investigations of cellular automata with regard to their ability to accept inputs under certain time constraints, in this paper we are studying cellular automata with regard to their ability to generate strings in real time. Structural properties such as speedup results and closure properties are investigated. On the one hand, c...

We study the computational and descriptional complexity of self-verifying pushdown automata (SVPDA) and self-verifying realtime queue automata (SVRQA). A self-verifying automaton is a nondeterministic device whose nondeterminism is symmetric in the following sense. Each computation path can give one of the answers yes, no, or do not know. For every...

A two-sided extension of strictly locally testable languages is presented. In order to determine membership within a two-sided strictly locally testable language, the input must be scanned from both ends simultaneously, whereby it is synchronously checked that the factors read are correlated with respect to a given binary relation. The class of two...

To determine the computational capacity of cellular automata they are often investigated towards their ability to accept formal languages within certain time constraints. In this paper, we take up an opposite position and look at cellular automata towards their ability to generate formal languages, here called patterns, within certain time constrai...

The model of deterministic input-driven multi-counter automata is introduced and studied. On such devices, the input letters uniquely determine the operations on the underlying data structure that is consisting of multiple counters. We study the computational power of the resulting language families and compare them with known language families ins...

We consider the model of an iterated uniform finite-state transducer, which executes the same length-preserving transduction in iterative sweeps. The first sweep takes place on the input string, while any subsequent sweep works on the output of the previous one. We focus on unary languages.

We introduce the deterministic computational model of an iterated uniform finite-state transducer (iufst). An iufst performs the same length-preserving transduction on several left-to-right sweeps. The first sweep takes place on the input string, while any other sweep processes the output of the previous one. The iufst accepts by halting at the end...

part : TC 1: Foundations of Computer Science

Partial word finite automata are deterministic finite automata that may have state transitions on a special symbol \(\diamond \) which represents an unknown symbol or a hole in the word. Together with a subset of the input alphabet that gives the symbols which may be substituted for the \(\diamond \), a partial word finite automaton represents a re...

Input-driven pushdown automata (IDPDA) are pushdown automata where the next action on the pushdown store (push, pop, nothing) is solely governed by the input symbol. Nowadays such devices are usually defined such that popping from the empty pushdown does not block the computation but continues it with empty pushdown. Here, we consider IDPDAs that h...

It is well known that reversible finite automata do not accept all regular languages, that reversible pushdown automata do not accept all deterministic context-free languages, and that reversible queue automata are less powerful than deterministic real-time queue automata. It is of significant interest from both a practical and theoretical point of...

An iterated uniform finite-state transducer executes the same length-preserving transduction in iterative sweeps. The first sweep occurs on the input string, while any subsequent sweep works on the output of the previous one. We consider devices with one-way motion and two-way motion, i.e., sweeps are either from left to right only, or alternate fr...

In contrast to many investigations of cellular automata with regard to their ability to accept inputs under certain time constraints, we are studying here cellular automata towards their ability to generate strings in real time. Structural properties such as speed-up results and closure properties are investigated. On the one hand, constructions fo...

An iterated uniform finite-state transducer (\(\textsc {iufst}\)) operates the same length-preserving transduction, starting with a sweep on the input string and then iteratively sweeping on the output of the previous sweep. The \(\textsc {iufst}\) accepts or rejects the input string by halting in an accepting or rejecting state along its sweeps. W...

Reversible computation allows computation to proceed not only in the standard, forward direction, but also backward, recovering past states. While reversible computation has attracted interest for its multiple applications, covering areas as different as low-power computing, simulation, robotics and debugging, such applications need to be supported...

While the closure of a language family \(\mathscr {L}\) under certain language operations is the least family of languages which contains all members of \(\mathscr {L}\) and is closed under all of the operations, a kernel of \(\mathscr {L}\) is a greatest family of languages which is a subfamily of \(\mathscr {L}\) and is closed under all of the op...

This book constitutes the refereed proceedings of the workshops which complemented the 23rd Symposium on Formal Methods, FM 2019, held in Porto, Portugal, in October 2019. This volume presents the papers that have been accepted for the following workshops: Third Workshop on Practical Formal Verification for Software Dependability, AFFORD 2019; 8th...

This book constitutes the refereed proceedings of the workshops which complemented the 23rd Symposium on Formal Methods, FM 2019, held in Porto, Portugal, in October 2019. This volume presents the papers that have been accepted for the following workshops: Third Workshop on Practical Formal Verification for Software Dependability, AFFORD 2019; 8th...

We introduce the concept of one-time nondeterminism as a new kind of limited nondeterminism for finite state machines and pushdown automata. Roughly speaking, one-time nondeterminism means that at the outset the computation is nondeterministic, but whenever it performs a guess, this guess is fixed for the rest of the computation. We characterize th...

Finite state machines are investigated towards their ability to reversibly compute transductions, that is, to transform inputs into outputs in a reversible way. This means that the transducers are backward deterministic and hence are able to uniquely step the computation back and forth. The families of transductions computed are classified with reg...

The model of deterministic input-driven multi-counter automata is introduced and studied. On such devices, the input letters uniquely determine the operations on the underlying data structure that is consisting of multiple counters. We study the computational power of the resulting language families and compare them with known language families ins...

We introduce the deterministic computational model of an iterated uniform finite-state transducer (iufst). A iufst performs the same length-preserving transduction on several left-to-right sweeps. The first sweep takes place on the input string, while any other sweep processes the output of the previous one. The iufst accepts or rejects upon haltin...

We briefly summarize some of the findings on non-recursive trade-offs, which were first observed by Meyer and Fischer in their seminal paper on “Economy of Description by Automata, Grammars, and Formal Systems” in 1971. This general phenomenon is about conversion problems between different (computational) description models that cannot be solved ef...

We study the computational capacity of self-verifying iterative arrays (). A self-verifying device is a nondeterministic device whose nondeterminism is symmetric in the following sense. Each computation path can give one of the answers yes, no, or do not know. For every input word, at least one computation path must give either the answer yes or no...

Iterative arrays whose internal inter-cell communication is quantitatively restricted are investigated. The quantity of communication is measured by counting the number of uses of the links between cells. In particular, iterative arrays are studied where the maximum number of communications per cell occurring in accepting computations is drasticall...

Classical string assembling systems form computational models that generate strings from copies out of a finite set of assembly units. The underlying mechanism is based on piecewise assembly of a double-stranded sequence of symbols, where the upper and lower strand have to match. The generative power of such systems is driven by the power of the ma...

Different types of subregular expressions are studied. Each type is obtained by either omitting one of the regular operations or replacing it by complementation or intersection. For uniformity and in order to allow non-trivial languages to be expressed, the set of literals is a finite set of words instead of letters. The power and limitations as we...

We introduce and study the model of diving queue automata which are basically finite automata equipped with a storage medium that is organized as a queue. Additionally, two queue heads are provided at both ends of the queue that can move in a read-only mode inside the queue. In particular, we consider suitable time constraints and the case where on...

We consider jumping finite automata and their operational state complexity and decidability status. Roughly speaking, a jumping automaton is a finite automaton with a non-continuous input. This device has nice relations to semilinear sets and thus to Parikh images of regular sets, which will be exhaustively used in our proofs. In particular, we pro...

Various synchronization algorithms have been introduced in literature during the last decades to deal with the firing squad synchronization problem on cellular automata (CA). Among others defective CA algorithms, where the CA cell is able to transmit information without previous processing, have been also presented. In our case, originating from th...

We study the computational capacity of self-verifying cellular automata with an emphasis on one-way information flow (). A self-verifying device is a nondeterministic device where each computation path can give one of the answers yes, no, or do not know. For every input word, at least one computation path must give either the answer yes or no, and...

We investigate finite automata whose state graphs are undirected. This means that for any transition from state p to q consuming some letter a from the input there exists a symmetric transition from state q to p consuming a letter a as well. So, the corresponding language families are subregular and, in particular in the deterministic case, subreve...

Motivated by preprocessing devices occurring for example in the context of syntactic parsers or HTML sanitization, we study pairs of finite state transducers and deterministic machines such as pushdown automata or queue automata as language accepting devices, where the original input is translated by a finite state transducer to an input of the det...

String assembling systems are biologically inspired mechanisms that generate strings from copies out of finite sets of assembly units. The underlying mechanism is based on piecewise assembly of a double-stranded sequence of symbols, where the upper and lower strand have to match. The generation is additionally controlled by the requirement that the...

A queue automaton is basically a finite automaton equipped with a storage obeying the first-in-first-out principle, a queue. The power of queue automata has been studied from several perspectives. One of the classical results frequently cited in the literature is that a machine equipped with a queue storage can be capable of universal computations....

We give a survey on the descriptional complexity of cellular models including one-way and two-way cellular automata, iterative arrays, and models with a fixed number of cells. For the former models so-called non-recursive trade-offs can be shown, that is, the savings in size that such automata may provide are not bounded by any recursive function....

We study reversible deterministic finite automata (REV-DFAs), that are partial deterministic finite automata whose transition function induces an injective mapping on the state set for every letter of the input alphabet. We give a structural characterization of regular languages that can be accepted by REV-DFAs. This characterization is based on th...

We investigate cellular automata as acceptors for formal languages. In particular, we consider real-time one-way cellular automata ((Formula presented.)) with the additional property that during a computation any cell of the (Formula presented.) has the ability to dissolve itself, so-called shrinking one-way cellular automata ((Formula presented.))...

A k-limited automaton is a linear bounded automaton that may rewrite each tape cell only in the first k visits, where k≥0 is a fixed constant. It is known that these automata accept context-free languages only. We investigate the descriptional complexity of limited automata. Since the unary languages accepted are necessarily regular, we first study...

We investigate the descriptional complexity of operations on semilinear sets. Roughly speaking, a semilinear set is the finite union of linear sets, which are built by constant and period vectors. The interesting parameters of a semilinear set are: (i) the maximal value that appears in the vectors of periods and constants and (ii) the number of suc...

We introduce and study input-driven deterministic and nondeterministic double-head pushdown automata. A double-head pushdown automaton is a slight generalization of an ordinary pushdown automaton working with two input heads that move in opposite directions on the common input tape. In every step one head is moved and the automaton decides on accep...

Recently, a method to decide the NL-complete problem of whether the language accepted by a given deterministic finite automaton (DFA) can also be accepted by some reversible deterministic finite automaton (REV-DFA) has been derived. Here, we show that the corresponding problem for nondeterministic finite automata (NFA) is PSPACE-complete. The recen...

We introduce and investigate stack transducers, which are one-way stack automata with an output tape. A one-way stack automaton is a classical pushdown automaton with the additional ability to move the stack head inside the stack without altering the contents. For stack transducers, we distinguish between a digging and a non-digging mode. In diggin...

We consider jumping finite automata and their operational state complexity and decidability status. Roughly speaking, a jumping automaton is a finite automaton with a non-continuous input. This device has nice relations to semilinear sets and thus to Parikh images of regular sets, which will be exhaustively used in our proofs. In particular, we pro...

We introduce the concept of one-time nondeterminism as a new kind of limited nondeterminism for finite state machines and pushdown automata. Roughly speaking, one-time nondeterminism means that at the outset the automaton is nondeterministic, but whenever it performs a guess, this guess is fixed for the rest of the computation. We characterize the...

Finite state machines are investigated towards their ability to reversibly compute transductions, that is, to transform inputs into outputs in a reversible way. This means that the transducers are backward deterministic and hence are able to uniquely step the computation back and forth. The families of transductions computed are classified with reg...

By former and recent results the model of reversible deterministic finite automata is well understood. On the other hand, reversible nondeterministic finite automata and their accepted languages have not systematically been considered in the literature. Here it turns out that reversible nondeterministic finite automata (\(\text {REV-NFA}\)s) are mo...

We investigate cellular automata that are composed of reversible components with regard to the recognition of formal languages. In particular, real-time one-way cellular automata (\(\text {OCA}\)) are considered which are composed of reversible Mealy automata. Moreover, we differentiate between three notions of reversibility in the Mealy automata,...

We investigate chop operations, which can be seen as generalized concatenation. For several language families of the Chomsky hierarchy we prove (non)closure properties under chop operations and incomparability to the family of languages that are the chop of two regular languages. We also prove non-closure of that language family under Boolean opera...

One-way multi-head finite automata are considered towards their ability to perform reversible computations. It is shown that, for every number of heads, there are problems which can be solved by one-way k-head finite automata, but not by any one-way reversible k-head finite automaton. Additionally, a proper head hierarchy is obtained for one-way re...

We investigate subfamilies of context-free languages that share two important properties. The languages are accepted by input-driven pushdown automata as well as by a reversible pushdown automata. So, the languages are input driven and reversible at the same time. This intersection can be defined on the underlying language families or on the underl...

The firing squad synchronization problem on Cellular Automata (CA) has been studied extensively for many years, and a rich variety of synchronization algorithms have been proposed. From Mazoyer’s paper it is known that a minimal-time solution with 6 states exists. The firing squad synchronization problem has also been studied for defective CA where...

The expressive capacity of three different types of regular expressions without concatenation is studied. In particular, we consider alphabetic concatenation-free expressions, which are ordinary regular expressions without concatenation, simple concatenation-free expressions, where the set of literals is a finite set of words instead of letters, an...

Recently, Holzer et al. gave a method to decide whether the language accepted by a given deterministic finite automaton (DFA) can also be accepted by some reversible deterministic finite automaton (REV-DFA), and eventually proved NL-completeness. Here, we show that the corresponding problem for nondeterministic finite state automata (NFA) is PSPACE...

We introduce and investigate stack transducers, which are one-way stack automata with an output tape. A one-way stack automaton is a classical pushdown automaton with the additional ability to move the stack head inside the stack without altering the contents. For stack transducers, we distinguish between a digging and a non-digging mode. In diggin...

It is well known that reversible finite automata do not accept all regular languages and that reversible pushdown automata do not accept all deterministic context-free languages. It is of significant interest both from a practical and theoretical point of view to close these gaps. We here extend these reversible models by a preprocessing unit which...

We investigate the descriptional complexity of the subregular language classes of (strongly) bounded regular languages. In the first part, we study the costs for the determinization of nondeterministic finite automata accepting strongly bounded regular languages. The upper bound for the costs is larger than the costs for determinizing unary regular...

For input-driven queue automata (\(\text {IDQA}\)) the input alphabet is divided into three distinct classes and the actions on the queue (enter, remove, nothing) are solely governed by the input symbols. Here, this model is extended in such a way that the input of an \(\text {IDQA}\) is preprocessed by an internal deterministic sequential transduc...

The deterministic shrinking two-pushdown automata characterize the deterministic growing context-sensitive languages, known to be the Church-Rosser languages. Here, we initiate the investigation of reversible two-pushdown automata, RTPDAs, in particular the shrinking variant. We show that as with the deterministic version, shrinking and length-redu...

We consider the model of deterministic set automata which are basically deterministic finite automata equipped with a set as an additional storage medium. The basic operations on the set are the insertion of elements, the removing of elements, and the test whether an element is in the set. We investigate the computational power of deterministic set...

Iterative arrays with set storage (SIA) are one-dimensional arrays of interconnected interacting finite automata. The input is supplied sequentially to the distinguished communication cell at the origin. In addition, the communication cell controls a set storage. To this end, it is equipped with a one-way writing tape where strings for the set oper...

Systems of deterministic finite automata communicating by sending their states upon request are investigated, when the amount of communication is restricted, that is, when the number of necessary communications during the computations of the system is bounded by a function depending on the length of the input. The computational power and decidabili...

## Citations

... 2.5]. Several classical methods can be applied in order to switch between the representation of X by an automaton or by a corresponding regular expression [10,33]. Furthermore, every regular subset of A * can be described by a so-called unambiguous regular expression, which is exclusively built from unambiguous regular ...

... Cellular automata have long been used for construction of cryptographic primitives [7][8][13][14][15][16][17][18][19][20][21]. Frequently, the elementary one-dimensional cellular automata are used for generation of binary pseudo-random sequences, which have decent statistical characteristics [14][15][16][17][18][19]. ...

... Deterministic pushdown transducers have also been introduced, and analysed with respect to their ability to compute reversible transductions [66]. Now, the families of transductions computed are classified with regard to four types of length-preserving transductions as well as to the property of working reversibly. ...

Reference: Foundations of Reversible Computation

... The model DFAwtl is extended by now in such a way that the input is preprocessed by an FST. Our model is motivated by [17,18] where various types of pushdown automata had such a preprocessed input. We are ready to give a formal definition of our new cascade/combo automata. ...

... Cellular automata have long been used for construction of cryptographic primitives [7][8][13][14][15][16][17][18][19][20][21]. Frequently, the elementary one-dimensional cellular automata are used for generation of binary pseudo-random sequences, which have decent statistical characteristics [14][15][16][17][18][19]. ...

... This is an interesting class of languages containing, e.g., all even linear languages [2,14,16]. Even linear and other special subclasses of linear context-free languages are of recent interests of various research papers, see, e.g., [7,11,29], due to their learnability property in formal languages [4,28]. Here, the accepted language classes of various restricted classes of WK automata and their relations are analyzed showing a finer hierarchy than the previous model has provided. ...

... The computational and descriptional complexity of selfverifying pushdown automata has been studied in Fernau et al. (2017). Self-verifying cellular automata have recently been introduced in Kutrib and Worsch (2020), where it turned out that realtime self-verifying one-way cellular automata (SVOCA) are strictly more powerful than realtime deterministic one-way cellular automata, since they can accept non-semilinear unary languages. ...

... From this point of view, CAs compute a (partial) function mapping an initial length n to a string of length n over some alphabet. First investigations for this model have been made in [7]. In particular, the real-time generation of unary patterns is studied in depth and a characterization by time-constructible functions and their corresponding unary formal languages is given. ...

Reference: String Generation by Cellular Automata

... The notion of an iterated uniform finite-state transducer (IUFST) has been introduced in [2] (see [3] for the journal version) and can be described as a finite transducer that iteratively sweeps from left to right over the input tape while performing the same length-preserving transduction. In particular, the output of the previous sweep is taken as input for every new sweep. ...

... In Sect. 8, as typically done in the literature for formalisms defining regular languages (see, e.g., [3,4,6,16,19,[22][23][24]), the problem of establishing the size cost of implementing boolean language operations on constant length dqas and nqas is tackled. As a useful tool in this investigation, analogously to what is done for constant height pushdown automata [3][4][5][6]17], a normal form for constant length queue automata is defined, where at most one symbol is enqueued on each move. ...