Andreas Malcher

Justus-Liebig-Universität Gießen | JLU · Institut für Informatik

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...

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...

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...

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...

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...

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 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...

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...

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...

Insertion systems or insertion grammars are a generative formalism in which words can only be generated by starting with some axioms and by iteratively inserting strings subject to certain contexts of a fixed maximal length. It is known that languages generated by such systems are always context sensitive and that the corresponding language classes...

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...

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...

Iterative arrays with restricted internal inter-cell communication are investigated. A quantitative measure for the communication is defined by counting the number of uses of the links between cells and it is differentiated between the sum of all communications of an accepting computation and the maximum number of communications per cell occurring...

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...

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...

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 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 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...

Iterative arrays with restricted internal inter-cell communication are investigated. A quantitative measure for the communication is defined by counting the number of uses of the links between cells and it is differentiated between the sum of all communications of an accepting computation and the maximum number of communications per cell occurring...

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 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.))...

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...

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...

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,...

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...

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...

In input-driven pushdown automata (\(\text {IDPDA}\)) the input alphabet is divided into three distinct classes and the actions on the pushdown store (push, pop, nothing) are solely governed by the input symbols. Here, this model is extended in such a way that the input of an \(\text {IDPDA}\) is preprocessed by a deterministic sequential transduce...

Reversible Turing machines with a working tape and a one-way or two-way read-only input tape are considered. We investigate the classes of languages acceptable by such devices with small time bounds in the range between real time and linear time, i.e., time bounds of the form \(n+r(n)\) where \(r\in o(n)\) is a sublinear function. It is shown that...

We investigate cellular automata as acceptors for formal languages. In particular, we consider real-time one-way cellular automata (\(\text {OCA}\)) with the additional property that during a computation any cell of the \(\text {OCA}\) has the ability to dissolve itself and we call this model shrinking one-way cellular automata (\(\text {SOCA}\))....

We introduce and study the model of deterministic input-driven queue automata. On such devices, the input letters uniquely determine the operations on the memory store which is organized as a queue. In particular, we consider the case where only a finite number of turns on the queue is allowed. The resulting language families share with regular lan...

Stateless variants of deterministic one-way multi-head finite automata with pebbles, that is, automata where the heads can drop, sense, and pick up pebbles, are studied. The relation between heads and pebbles is investigated, and a proper double hierarchy concerning these two resources is obtained. Moreover, it is shown that a conversion of an arbi...

We investigate the descriptional complexity of deterministic one-way multi-head finite automata accepting unary languages. It is known that in this case the languages accepted are regular. Thus, we study the increase of the number of states when an n-state k-head finite automaton is simulated by a classical (one-head) deterministic or nondeterminis...

Unary deterministic one-way multi-head finite automata characterize the unary regular languages. Here they are studied with respect to the existence of head and state hierarchies. It turns out that for any fixed number of states, there is an infinite proper head hierarchy. In particular, the head hierarchy for stateless deterministic one-way multi-...

We investigate the descriptional complexity and decidability of obliviousness for two-way finite automata. In particular, we consider the simulation of two-way deterministic finite automata (2DFAs) by oblivious 2DFAs, the simulation of oblivious 2DFAs by sweeping 2DFAs and one-way nondeterministic finite automata (1NFAs) as well as the simulation o...

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...

We consider systems of interacting finite automata. On the one hand, we look at automata systems consisting of a small constant number of synchronous and autonomous finite automata that share a common input and communicate with each other as weakly parallel models. On the other hand, we consider cellular automata consisting of a huge number of inte...

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...

The descriptional complexity of deterministic and nondeterministic set automata is investigated. Set automata are basically 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 or not an element is in the set. We show that r...

Real-time one-way cellular automata (\({\text {OCA}}\)) are investigated towards their ability to perform reversible computations with regard to formal language recognition. It turns out that the standard model with fixed boundary conditions is quite weak in terms of reversible information processing, since it is shown that in this case exactly the...

Systems of deterministic finite automata communicating by sending their states upon request are investigated, when the amount of communication is restricted. The computational power and decidability properties are studied for the case of returning centralized systems, when the number of necessary communications during the computations of the system...

We provide a new construction of a nondeterministic finite automaton (NFA) accepting the pushdown store language of a given pushdown automaton (PDA). The resulting NFA has a number of states which is quadratic in the number of states and linear in the number of pushdown symbols of the given PDA. Moreover, we prove the size optimality of our constru...

We introduce and study the model of input-driven queue automata. On such devices, the input letters uniquely determine the operations on the memory store which is organized as a queue. In particular, we consider the case where only a finite number of turns on the queue is allowed. The resulting language families share with regular languages many de...

Stateless variants of deterministic one-way multi-head finite automata with pebbles, that is, automata where the heads can drop, sense, and pick up pebbles, are studied. The relation between heads and pebbles is investigated, and a proper double hierarchy concerning these two resources is obtained. Moreover, it is shown that a conversion of an arbi...

The parallel models of cellular automata and iterative arrays are investigated towards their ability to compute transductions, that is, to transform inputs into outputs. The families of transductions computed are classified with regard to the time allowed to process the input and the output, respectively. The time complexities of real-time and line...

One-way multi-head finite automata are considered towards their ability to perform reversible computations. It is shown that, for every number k ≥ 1 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-...

We introduce and investigate input-driven stack automata, which are a generalization of input-driven pushdown automata that recently became popular under the name visibly pushdown automata. Basically, the idea is that the input letters uniquely determine the operations on the pushdown store. This can nicely be generalized to stack automata by furth...

We investigate the descriptional complexity of little resources added to deterministic one-dimensional real-time iterative arrays. More precisely, we study the impact of adding sublinearly more time obtaining time complexities strictly in between real time and linear time, adding dimensions, allow the communication cell to perform a few nondetermin...

Unary deterministic one-way multi-head finite automata characterize the unary regular languages. Here they are studied with respect to the existence of head and state hierarchies. It turns out that for any fixed number of states, there is an infinite proper head hierarchy. In particular, the head hierarchy for stateless deterministic one-way multi-...

Cellular automata are investigated towards their ability to compute transductions, that is, to transform inputs into outputs. The families of transductions computed are classified with regard to the time allowed to process the input and to compute the output. Since there is a particular interest in fast transductions, we mainly focus on the time co...

It is well known that the pushdown store language P(M) of a pushdown automaton (PDA) M — i.e., the language consisting of words occurring on the pushdown along accepting computations of M — is a regular language. Here, we design succinct nondeterministic finite automata (NFA) accepting P(M). In detail, an upper bound on the size of an NFA for P(M)...

The characterization of the class of FO[+]-definable languages by some generating or recognizing device is still an open problem. We prove that, restricted to word bounded languages, this class coincides with the class of semilinear languages. We also study the closure properties of the classes of languages definable in FO[+1], FO[<], FO[+] and FOC...

With this contribution we would like to commemorate Chandra M. R. Kintala, who passed away in November 2009. We will give short overviews of his CV and his contributions to the field of theoretical and applied computer science and, given the opportunity, will attempt to present his influence on areas like limited nondeterminism and resources as wel...

We investigate the descriptional complexity of little resources added to deterministic one-dimensional real-time iterative arrays. More precisely, we study the impact of adding sublinearly more time obtaining time complexities strictly in between real time and linear time, adding dimensions, allow the communication cell to perform a few nondetermin...

Systems of parallel finite automata communicating by states are investigated. We consider deterministic and nondeterministic devices and distinguish four working modes. It is known that systems in the most general mode are as powerful as one-way multi-head finite automata. Here we solve some open problems on the computational capacity of systems wo...

Parallel communicating finite automata (PCFAs) are systems of several finite state automata which process a common input string in a parallel way and are able to communicate by sending their states upon request. We consider deterministic and nondeterministic variants and distinguish four working modes. It is known that these systems in the most gen...

Two-way nondeterministic pushdown automata (2PDA) are classical nondeterministic pushdown automata (PDA) enhanced with two-way motion of the input head. In this paper, the subclass of 2PDA accepting bounded languages and making at most a constant number of input head turns is studied with respect to descriptional complexity aspects. In particular,...

A d-dimensional cellular automaton is a d-dimensional grid of interconnected interacting finite automata. There are models with parallel and sequential input modes. In the latter case, the distinguished automaton at the origin, the communication cell, is connected to the outside world and fetches the input sequentially. Often in the literature this...

Multi-head finite automata were introduced and first investigated by Rabin and Scott in 1964 and Rosenberg in 1966. Since that time, a vast literature on computational and descriptional complexity issues on multi-head finite automata documenting the importance of these devices has been developed. Although multi-head finite automata are a simple con...

Cellular automata and iterative arrays are one-dimensional arrays of interconnected interacting finite automata which work synchronously at discrete time steps. In this paper, the focus lies on the resource of communication which naturally takes place between cells. Communication is measured here with regard to qualitative and quantitative aspects....

Iterative arrays (IAs) are a parallel computational model with a sequential processing of the input. They are one-dimensional arrays of interacting identical deterministic finite automata. In this paper, realtime-IAs with sublinear space bounds are used to recognize formal languages. The existence of an infinite proper hierarchy of space complexity...

We investigate synchronous systems consisting of two finite automata running in opposite directions on a shared read-only input. The automata communicate by sending messages. The communication is quantitatively measured by the number of messages sent during a computation. It is shown that even the weakest non-trivial devices in question, that is, s...

With this contribution we would like to remember Chandra M. R. Kintala who passed away in November 2009. We will give short overviews of his CV and his contributions to the field of theoretical and applied computer science and, given the opportunity, will attempt to present the current state of limited nondeterminism and limited resources for machi...

Reversible pushdown automata are deterministic pushdown automata having the property that any configuration occurring in any computation has exactly one predecessor. In this paper, the computational capacity of reversible computations in pushdown automata is investigated and turns out to lie properly in between the regular and deterministic context...

The characterization of the class of FO[ + ]-definable languages by some generating or recognizing device is still an open problem. We prove that, restricted to bounded languages, this class coincides with the class of semilinear languages. We also study some closure properties of FO[ + ]-definable languages which, as a by-product, allow us to give...

International audience We investigate the descriptional complexity of basic operations on real-time one-way cellular automata with an unbounded as well well as a fixed number of cells. The size of the automata is measured by their number of states. Most of the bounds shown are tight in the order of magnitude, that is, the sizes resulting from the e...

Cellular automata are one-dimensional arrays of interconnected interacting finite automata, also called cells. Here, we investigate one of the weakest class of cellular automata, namely the class of real-time one-way cellular automata. Additionally, we impose two restrictions on the inter-cell communication. First, the number of allowed uses of the...

A generalization of pushdown automata towards regulated nondeterminism is studied. The nondeterminism is governed in such a way that the decision, whether or not a nondeterministic rule is applied, depends on the whole content of the stack. More precisely, the content of the stack is considered as a word over the stack alphabet, and the pushdown au...