
klaus-joern Lange- University of Tübingen
klaus-joern Lange
- University of Tübingen
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Publications (99)
We build a notion of algebraic recognition for visibly pushdown languages by finite algebraic objects. These come with a typical Eilenberg relationship, now between classes of visibly pushdown languages and classes of finite algebras. Building on that algebraic foundation, we further construct a topological object with one purpose being the possibi...
Logical formulas are naturally decomposed into their subformulas and circuits into their layers. How are these decompositions expressed in a purely language-theoretical setting? We address that question, and in doing so, introduce a product directly on languages that parallels formula composition. This framework makes an essential use of languages...
We extend the familiar program of understanding circuit complexity in terms of regular languages to visibly counter languages. Like the regular languages, the visibly counter languages are \(\mathrm {NC}^{1}\)- complete. We investigate what the visibly counter languages in certain constant depth circuit complexity classes are. We have initiated thi...
We obtain results within the area of dense completeness, which describes a close relation between families of formal languages and complexity classes. Previously we were able show that this relation exists between counter languages and \(\mathbf {NL}\) but not between the regular languages and \(\mathbf {NC^1}\).
We narrow the gap between the regul...
We examine visibly counter languages, which are languages recognized by visibly counter automata (a.k.a. input driven counter automata). We are able to effectively characterize the visibly counter languages in AC0 and show that they are contained in FO[+].
We show that every language accepted by a nondeterministic auxiliary pushdown automaton in polynomial time (that is, every language in SAC¹ = Log(CFL)) can be accepted by a symmetric auxiliary pushdown automaton in polynomial time.
The effect of severely tightening the uniformity of Boolean circuit families is investigated. The impact on NC 1 and its subclasses is shown to depend on the characterization chosen for the class, while classes such as P appear to be more robust. Tightly uniform subclasses of NC 1 whose separation may be within reach of current techniques emerge.
We introduce dense completeness, which gives tighter connection between formal language classes and complexity classes than the usual notion of completeness. A family of formal languages \(\mathcal F\) is densely complete in a complexity class \(\mathcal C\) iff \({\mathcal F}\subseteq{\mathcal C}\) and for each \(C \in{\mathcal C}\) there is an \(...
The Boolean formula value problem asks for the Boolean output value of a given input formula. We code it as a formal language \(\ensuremath{{\cal D_+}}\subset\{a,b\}^*\). \({\cal D_+}\) is a nonregular, visibly pushdown language. We give automata for \({\cal D_+}\) which enable us to derive some of its syntactic equations. It is unknown whether the...
We show that every language accepted by a nondeterministic auxiliary pushdown automaton in polynomial time (that is, every language in SAC<sup>1</sup> = Log(CFL)) can be accepted by a symmetric auxiliary pushdown automaton in polynomial time.
The membership problems of both stack automata and nonerasing stack automata are shown to be complete for polynomial time.
Die Dyck-Sprachen sind ein Grundbegriff aus dem Bereich der formalen Sprachen. Ausgehend von der Person des Namensgebers werden ihre Geschichte und ihre Bedeutung in der theoretischen Informatik in diesem Überblick dargestellt.
We characterize the languages in TC0 = L(Maj[<,Bit]) and L(Maj[<]) as inverse morphic images of certain groups. Necessarily these are infinite, since nonregular
sets are concerned. To limit the power of these infinite algebraic objects, we equip them with a finite type set and introduce
the notion of a finitely typed (infinite) monoid. Following th...
In this work a complete problem for an unambiguous logspace class is presented. This is surprising since unambiguity is a `promise' or `semantic' concept. These usually lead to classes apparently without complete problems. 1 Introduction One of the most central questions of complexity theory is to compare determinism with nondeterminism. Our inabil...
Two characterizations of the logarithmic alternation hierarchy are given. The first one by bounded quantification of DSPACE(log n)-predicates, where the quantified words are given as one-way input. It is shown that a simple change of the order of the quantified words (w.r.t. the order of the quantifiers) allows the generation of NP-complete sets. T...
The notions of weak and strong unambiguity of augmented push-down automata are considered and related to unambiguities of circuits. In particular we exhibit circuit classes exactly characterizing polynomially time bounded unambiguous augmented push-down automata. Introduction An important object in parallel complexity theory, the class NC , can be...
The complexity of languages generated by context-free grammars with disconnecting is investigated. It is shown that even linear and deterministic context-free languages can generate languages of multisets, the membership problem of which is NP-complete. In contrast to that, this problem is in DSPACE(log n) for regular sets.
The complexities of problems related to automata with storages, an abstract automaton model introduced by Engelfriet, are analyzed. In particular, we show a close relationship between the word problem of two-way automata and the emptiness problem of one-way automata. Moreover, we give some hardest languages for classes of languages accepted by some...
We consider language families obtained from context-free languages by complete cancellation of substrings from the Dyck language with one pair of parentheses. The class of such languages contains languages with arbitrary exponential growth, the Petri net languages, and NP-complete sets.
We show that
AS2LA\Sigma _2^\mathcal{L}
coincides with
AP2LA\Pi _2^\mathcal{L}
. Essentially this is done by Hausdorff reducing the
AS2LA\Sigma _2^\mathcal{L}
-complete set (GAPCo-GAP)(AS2L = Lhd (NL)A\Sigma _2^\mathcal{L} = \mathcal{L}_{hd} (N\mathcal{L})
.
Uniformity notions more restrictive than the usual FO[<, +, *]-uniformity = FO[<, Bit]-uniformity are introduced. It is shown that the general framework exhibited by Barrington et al. still holds if the fan-in of the gates in the corresponding circuits is considered
It is well-known that the Σk- and Πk-levels of the dot-depth hierarchy and the polynomial hierarchy correspond via leaf languages. We extend this correspondence to the Δk-levels of these hierarchies: ${\rm Leaf}^{\rm P} (\Delta_k^L) = \Delta_k^p$. The same methods are used to give evidence against an earlier conjecture of Straubing and Thérien abou...
The class of languages definable by majority quantifiers using the order predicate is investigated. It is shown that the additional use of first order or counting quantifiers does not increase this class. Further on, addition is in this connection a definable numerical predicate, while the converse does not hold. The emptiness problem for this clas...
The leaf-language mechanism associates a complexity class to a class of regular languages. It is well-known that the Σ
k
- and Π
k
-levels of the dot-depth hierarchy and the polynomial hierarchy correspond in this formalism. We extend this correspondence
to the Δ
k
-levels of these hierarchies: LeafP(ΔkL_{k}^{L}) = Δkp_{k}^{p}. These results are ob...
The Cayley group membership problem (CGM) is to input a groupoid (binary algebra) G given as a multiplication table, a subset X of G, and an element t of G and to determine whether t can be expressed as a product of elements of X. For general groupoids CGM is P-complete, and for associative algebras (semigroups) it is NL-complete. Here we investiga...
We present a deterministic algorithm running in space O , log n= log log n # solving the connectivity problem on strongly unambiguous graphs. In addition, we presentanO#log n# time-bounded algorithm for this problem running on a parallel pointer machine.
This paper describes the simulation of an S(n) space-bounded deterministic Turing machine by a reversible Turing machine operating in space S(n). It thus answers a question posed by C. H. Bennett [SIAM J. Comput. 18, No. 4, 766-776 (1989; Zbl 0676.68010)] and refutes the conjecture, made by M. Li and P. Vitányi [Proc. R. Soc. Lond., Ser. A 452, No....
We introduce the notions of control and communication structures in PRAM computations and relate them to the concept of data independence. Our main result is to characterize differences between unbounded fan-in parallelism ACk, bounded fan-in parallelism NCk, and the sequential classes DSPACE(logn) and LOGDCFL in terms of a PRAM's communication str...
. We locate the complexities of evaluating, of inverting, and of testing membership in the image of, morphisms h : Sigma ! Delta . By and large, we show these problems complete for classes within NL. Then we develop new properties of finite codes and of finite sets of words, which yield image membership subproblems that are closely tied to the unam...
S On the Power of Randomized Branching Programs Farid Ablayev Kazan University (joint work with Marek Karpinski, Universitat Bonn) We define a notion of randomized branching programs in a natural way similar to the notion of randomized circuits. We present two explicit boolean functions f n : f0; 1g 4n ! f0; 1g and g n : f0; 1g n ! f0; 1g such that...
We locate the complexities of evaluating, of inverting, and of testing membership in the image of, morphisms h : \Sigma ! \Delta . By and large, we show these problems complete for classes within NL. Then we develop new properties of finite codes and of finite sets of words, which yield image membership subproblems that are closely tied to the unam...
We present a deterministic algorithm running in space O(log2n /log log n ) solving the connectivity problem on strongly unambiguous graphs. In addition, we present an O(log n ) time-bounded algorithm for this problem running on a parallel pointer machine.
We present a deterministic algorithm running in space O(log(2) n/log log n) solving the connectivity problem on strongly unambiguous graphs. In addition, we present an O (log n) time-bounded algorithm for this problem running on a parallel pointer machine.
This paper discusses some aspects of implementing parallel algorithms on distributed computer systems like a LAN-connected set of workstations. The notions of parallel and distributed computing are represented by their interrelation. The possibility of distributed simulations of parallel models is discussed. Finally, the complexity theoretical cons...
We present a deterministic algorithm running in space O i log 2 n= log log n j solving the connectivity problem on strongly unambiguous graphs. In addition, we present an O(log n) time-bounded algorithm for this problem running on a parallel pointer machine. 1 Introduction A central challenge facing complexity theory is to relate determinism and no...
This paper describes the simulation of an S(n) space-bounded
deterministic Turing machine by a reversible Turing machine operating in
space S(n). It thus answers a question posed by C. Bennett (1989) and
refutes the conjecture, made by M. Li and P. Vitanyi (1996), that any
reversible simulation of an irreversible computation must obey Bennett's
rev...
of the monotone circuit value problem MCVP to LP 2 given in [1], one sees that the implementation of a "copy"-operation (besides the logical operators) is missing, which seems to be an essential ingredient of reductions of variants of CVP to graph problems, see, e.g., [4]. This leads to additional unwanted paths in the graph simulating the circuit....
Several new tree problems are shown complete for deterministic logarithmic space. These include the tree centroid problem and the tree isomorphism problem, which thus becomes the first isomorphism problem of a combinatorial nature shown complete for a fundamental resource-based complexity class. The crucial role of the input representation of trees...
This paper describes the simulation of an S(n) spacebounded deterministic Turing machine by a reversible Turing machine operating in space S(n). It thus answers a question posed by Bennett in 1989 and refutes the conjecture, made by Li and Vitanyi in 1996, that any reversible simulation of an irreversible computation must obey Bennett's reversible...
. We investigate complexities of insertion operations on formal languages relatively to complexity classes. In this way, we introduce operations closely related to LOG(CFL) and NP . Our results relativize and give new characterizations of the ways to relativize nondeterministic space. 1 Introduction There are many close connections between the theo...
This article discusses the existence of SymSPACE(logn)-complete formal languages. It is shown that a recent approach of Alvarez and Greenlaw to define symmetric versions of one-way
devices doesn't lead to SymSPACE(log n) complete problems when applied to linear context-free or to one-counter languages.
In this work a complete problem for an unambiguous logspace class is presented. This is surprising since unambiguity is a 'promise' or 'semantic' concept. These usually lead to classes apparently without complete problems.
In order to characterize certain formal languages capturing some syntactic aspects of higher programming languages we introduce automata with the storage type set, called set automata. We show the corresponding language class to have an NP-complete membership problem and a decidable emptiness problem. 1 Introduction One of the main issues of formal...
The following survey reviews some connections between formal languages and complexity theory. Families of formal languages are treated with complexity theoretical methods. In particular, the concept of unambiguity, common to both areas, is treated in detail. Some complexity theoretical aspects of operations on formal languages are indicated. This p...
We present a deterministic algorithm running in space O (log2
n/log log n) solving the connectivity problem on strongly unambiguous graphs. In addition, we present an O(log n) time-bounded algorithm for this problem running on a parallel pointer machine.
This paper concerns some of the theoretical complexity aspects of the reconfigurable network model. The computational power of the model is investigated under several variants, depending on the type of switches (or switch operations) assumed by the network nodes. Computational power is evaluated by focusing on the set of problems computable in cons...
We improve several upper bounds to the complexity of the membership problem for languages defined by iterated morphisms (D0L systems). The complexity bounds are expressed in terms of DLOGTIME-uniform circuit families. We prove: 1) For polynomially growing DOL systems the membership problem is contained in AC
0. 2) For arbitrary DOL systems the memb...
Several notions of deterministic linear languages are considered and compared with respect to their complexities and to the families of formal languages they generate. We exhibit close relationships between simple linear languages and the deterministic linear languages both according to Nasu and Honda and to Ibarra, Jiang, and Ravikumar. Determinis...
Languages defined by iterated homomorphisms, i.e., D0L systems, are closely related to the arithmetic of small numbers. Based on this interrelation we improve the upper bound NC 1 on the complexity of the membership problem for D0L systems. We prove that the membership problem is contained in a proper subclass of AC 0 . This will show that the D0L...
We introduce the notion of empty alternation by investigating alternating automata which are restricted to empty their storage except for a logarithmically space-bounded tape before making an alternating transition. In particular, we consider the cases when the depth of alternation is bounded by a constant or a polylogarithmic function. In this way...
The classes NC<sup>k</sup> and AC<sup>k</sup> are defined by
computational devices of polynomial size, i.e. by devices using a
polynomially bounded number of gates or processors. We consider the case
of exponential size, which results in classes between P and PSPACE. In
this way, we get new characterizations of P and UP. The resulting
relations of...
We introduce notions of control and communication structures for PRAM's and relate them to the concept of data-independence. Our main result is to characterize differences between unbounded fanin parallelism (i.e., the complexity classes AC
k
, k1), bounded fanin parallelism (i.e., the classes NC
k
, k1), and sequentialism (i.e., DSPACE(log n) an...
Several notions of deterministic linear languages are considered and compared with respect to their complexities and to the families of formal languages they generate. We exhibit close relationships between simple linear languages and the deterministic linear languages both according to Nasu and Honda and to Ibarra, Jiang, and Ravikumar. Determinis...
Some connections between formal languages and complexity are
reviewed. Families of formal languages are treated with complexity
theoretical methods. In particular, the concept of unambiguity, common
to both areas, is treated in detail. Some new results on deterministic
families of formal languages and on complexities of operations on formal
languag...
The concept of unambiguity of circuits is considered. Several classes of unambiguous circuit families within the NC-hierarchy are introduced and related to unambiguous automata and to PRAMs with exclusive write access. In particular, we show CREW-TIME(logkn) = UnambACk for each positive integer k.
We survey the efficiency of the ‘fast’ parallel algorithms for the recognition and ranking of context-free languages on the
Parallel Random Access Machine without write conflicts. The efficiency of the algorithm is the total number of operations
(the product of time and number of processors). Such efficiency depends heavily on the class of context-...
The emptiness problem for EOL systems is shown to be computationally equivalent to the word problem of RPAC automata which are augmented with a LOGSPACE working tape and a two-way input head.
We consider various types of unambiguity and fewness for log space bounded Turing machines and polynomial time bounded log space auxiliary pushdown automata. In particular, we introduce the notions of (general), reach, and strong unambiguity and fewness. We demonstrate that closure under complement of unambiguous classes implies equivalence of unam...
The concept of unambiguity of circuits is considered. Several
classes of unambiguous circuit families within the NC-hierarchy are
introduced and related to unambiguous automata and to PRAMs with
exclusive write-access. In particular, it is shown that CREW-TIME (log
n )=UnambAC
Nondeterministic reductions with a polynomial time bound or logarithmic space bound are characterized in terms of formal language operations like nonerasing homomorphisms and Kleene's star by relativizing the well-known equations NP=Log(H(Dspace(log n))), Nspace(log n)=Log(H(1-Dspace(log n))), and Nspace(log n)=Log(Dspace(log n)*). As corollaries w...
The complexity of languages generated by so-called context-free string grammars with disconnecting is investigated. The result is then applied to a number of graph grammar models with finite Church Rosser property. In particular, it is shown that these graph grammars can generate NP-complete languages.
Nondeterministic reductions with a polynomial time bound or logarithmic space bound are characterized in terms of formal language operations like nonerasing homomorphisms and Kleene's star by relativizing the well-known equations NP = LOG (H (DSPACE (log n))), NSPACE (log n) = LOG (H (1-DSPACE (log n))), and NSPACE (log n) = LOG (DSPACe (log n) *)....
Jones and Skyum in [J Sk 77], [J Sk 79], and [J Sk 81], as well as, van Leeuwen in [vL] and Sudborough in [Su77] classified the complexities of various problems concerning L systems. This was done by showing these problems, formulated as languages, to be complete for complexity classes like NSPACE(log n), DTIME(Poly), NTIME(Poly), or DSPACE(Poly) w...
We prove decidability results for recurrent words in T0L schemes and systems, thereby settling some recently posed open problems. However, the problems are shown to be Pspace-hard. These investigations are motivated by some questions from Markov DT0L systems.As the main tool for proving these results we introduce the notion of simultaneous growth,...
Non-deterministic two-tape automata as defined by Elgot and Mezei are similar to non-deterministic finite state acceptors — instead of reading from one tape, they can read simultaneously from two tapes. They accept just the rational subsets of X* Y*, and are closely related to linear context-free grammars. It is shown that, in contrast to the one-t...
Nondetermistic logspace-bounded reductions are introduced. A set in DSPACE(log n), NP-complete with respect to these reductions, is exhibited, which makes the transitive closure of the NLOG(·)-operation quite unlikely, unless NSPACE(log n) = NP is assumed. In contrast to this the NLOG-closure of NLOG(NLOG(·))-classes is shown.
The following results concerning context-free controlled ETOL systems are shown:
(CF)ETOL=(D
2)ETOL=(DCF)ETOL
(RMOL)EDTOL ⊂LOG(CF)
EOL ⪵ (CF)EDTOL
OI ∩ IO ⪵ (CF)ETOL
L homomorphisms, i.e. structure preserving mappings between OL systems, are introduced. Every L homomorphism is determined in a unique way by a homomorphism between thefree monoids generated by the alphabets of the related systems and by a nonnegative integer. Thereby the notion of L homomorphism is characterized in a decidable way. L homomorphisms...
The extension concept and the adult concept are shown to be equivalent for deterministic OL systems with at least two tables. This is done by showing the existance of a normal form for DTOL systems with respect to their adult languages.
We show the equivalence of deterministic auxiliary pushdown automata to owner write PRAMs in a fairly large setting by proving that DAuxPDA-TISP(f
O(1),log g) and CROW-TIPR(log f, g
o(1)) coincide. Such, we provide the first circuit characterizations of depth O(log f) for deterministic sequential automata which are f time-bounded.
We consider various types of unambiguity for logarithmic space bounded Turing machines and polynomial time bounded log space auxiliary push-down automata. In particular, we introduce the notions of (general), reach, and strong unambiguity. We demonstrate that closure under complement of unambiguous classes implies equivalence of unambiguity and "un...
Given m finite automata, the emptiness of intersection problem is to determine whether there exists a string which is accepted by all m automata. In the following we consider the case, when m is bounded by a function in the input length, i.e., in the size and number of the automata. In this way we get complete problems for nondeterministic space-bo...