Showing papers on "Pushdown automaton published in 2015"
TL;DR: It is shown that the minimum number of agents required to solve the ANTS problem crucially depends on the computational capabilities of the agents as well as the timing parameters of the execution environment.
53 citations
12 Oct 2015
TL;DR: Angluin’s \(L^*\) algorithm is harnessed for learning a deterministic finite automaton that describes the possible scenarios under which a given program error occurs and an abstract visual representation of errors and of program segments is presented.
Abstract: We propose to harness Angluin’s \(L^*\) algorithm for learning a deterministic finite automaton that describes the possible scenarios under which a given program error occurs. The alphabet of this automaton is given by the user (for instance, a subset of the function call sites or branches), and hence the automaton describes a user-defined abstraction of those scenarios. More generally, the same technique can be used for visualising the behavior of a program or parts thereof. This can be used, for example, for visually comparing different versions of a program, by presenting an automaton for the behavior in the symmetric difference between them, or for assisting in merging several development branches. We present initial experiments that demonstrate the power of an abstract visual representation of errors and of program segments.
38 citations
Posted Content•
TL;DR: It is shown that the computation of downward closures can be reduced to checking a certain unboundedness property and proved that downward closures are computable for every language class with effectively semilinear Parikh images that are closed under rational transductions.
Abstract: The downward closure of a word language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of any language is regular. While the downward closure appears to be a powerful abstraction, algorithms for computing a finite automaton for the downward closure of a given language have been established only for few language classes.
This work presents a simple general method for computing downward closures. For language classes that are closed under rational transductions, it is shown that the computation of downward closures can be reduced to checking a certain unboundedness property.
This result is used to prove that downward closures are computable for (i) every language class with effectively semilinear Parikh images that are closed under rational transductions, (ii) matrix languages, and (iii) indexed languages (equivalently, languages accepted by higher-order pushdown automata of order 2).
35 citations
01 Jan 2015
TL;DR: The equivalence between 2-limited automata and pushdown automata is investigated, and it is proved exponential upper and lower bounds for the sizes of push down automata simulating 2- limited automata are proved.
Abstract: Limited automata are one-tape Turing machines which are allowed to rewrite each tape cell only in the first d visits, for a given constant d. For each d ≥ 2, these devices characterize the class of context-free languages. We investigate the equivalence between 2-limited automata and pushdown automata, comparing the relative sizes of their descriptions. We prove exponential upper and lower bounds for the sizes of pushdown automata simulating 2-limited automata. In the case of the conversion of deterministic 2-limited automata into deterministic pushdown automata the upper bound is double exponential and we conjecture that it cannot be reduced. On the other hand, from pushdown automata we can obtain equivalent 2-limited automata of polynomial size, also preserving determinism. From our results, it follows that the class of languages accepted by deterministic 2-limited automata coincides with the class of deterministic context-free languages.
30 citations
06 Jul 2015
TL;DR: For language classes that are closed under rational transductions, it is shown that the computation of downward closures can be reduced to checking a certain unboundedness property in this paper.
Abstract: The downward closure of a word language is the set of all not necessarily contiguous subwords of its members It is well-known that the downward closure of any language is regular While the downward closure appears to be a powerful abstraction, algorithms for computing a finite automaton for the downward closure of a given language have been established only for few language classes
This work presents a simple general method for computing downward closures For language classes that are closed under rational transductions, it is shown that the computation of downward closures can be reduced to checking a certain unboundedness property
This result is used to prove that downward closures are computable for i every language class with effectively semilinear Parikh images that are closed under rational transductions, ii matrix languages, and iii indexed languages equivalently, languages accepted by higher-order pushdown automata of orderi¾?2
29 citations
Posted Content•
TL;DR: A tight EXPTIME complexity bound is obtained for a more restrictive subclass of PDA with timeless stack, thus subsuming the complexity bound known for dense-timed PDA.
Abstract: This paper contains two results on timed extensions of pushdown automata (PDA). As our first result we prove that the model of dense-timed PDA of Abdulla et al. collapses: it is expressively equivalent to dense-timed PDA with timeless stack. Motivated by this result, we advocate the framework of first-order definable PDA, a specialization of PDA in sets with atoms, as the right setting to define and investigate timed extensions of PDA. The general model obtained in this way is Turing complete. As our second result we prove NEXPTIME upper complexity bound for the non-emptiness problem for an expressive subclass. As a byproduct, we obtain a tight EXPTIME complexity bound for a more restrictive subclass of PDA with timeless stack, thus subsuming the complexity bound known for dense-timed PDA.
26 citations
06 Jul 2015
TL;DR: In this article, it was shown that the model of dense-timed pushdown automata with timeless stack is expressively equivalent to the one of PDA with infinite stack, and that the general model obtained in this way is Turing complete.
Abstract: This paper contains two results on timed extensions of pushdown automata (PDA). As our first result we prove that the model of dense-timed PDA of Abdulla et al. Collapses: it is expressively equivalent to dense-timed PDA with timeless stack. Motivated by this result, we advocate the framework of first-order definable PDA, a specialization of PDA in sets with atoms, as the right setting to define and investigate timed extensions of PDA. The general model obtained in this way is Turing complete. As our second result we prove NEXPTIME upper complexity bound for the non-emptiness problem for an expressive subclass. As a byproduct, we obtain a tight EXPTIME complexity bound for a more restrictive subclass of PDA with timeless stack, thus subsuming the complexity bound known for dense-timed PDA.
25 citations
01 Sep 2015
TL;DR: This work considers other formal models of concurrent systems with decidable safety problem and finds very liberal conditions on the individual processes under which the safety problem is decidable: the only substantial condition is the effective computability of the downward closure for the class of the leader processes.
Abstract: Verification of concurrent systems is a difficult problem in general, and this is the case even more in a parametrized setting where unboundedly many concurrent components are considered. Recently, Hague proposed an architecture with a leader process and unboundedly many copies of a contributor process interacting over a shared memory for which safety properties can be effectively verified. All processes in Hague's setting are pushdown automata. Here, we extend it by considering other formal models and, as a main contribution, find very liberal conditions on the individual processes under which the safety problem is decidable: the only substantial condition we require is the effective computability of the downward closure for the class of the leader processes. Furthermore, our result allows for a hierarchical approach to constructing models of concurrent systems with decidable safety problem: networks with tree-like architecture, where each process shares a register with its children processes (and another register with its parent). Nodes in such networks can be for instance pushdown automata, Petri nets, or multi-pushdown systems with decidable reachability problem.
24 citations
17 Aug 2015
TL;DR: It is shown that, for every full trio (a class of languages that is closed under rather weak operations) which has decidable diagonal problem, separability with respect to piecewise testable languages is decidable.
Abstract: The separability problem for word languages of a class \(\mathcal {C}\) by languages of a class \(\mathcal {S}\) asks, for two given languages I and E from \(\mathcal {C}\), whether there exists a language S from \(\mathcal {S}\) that includes I and excludes E, that is, \(I \subseteq S\) and \(S\cap E = \emptyset \). It is known that separability for context-free languages by any class containing all definite languages (such as regular languages) is undecidable. We show that separability of context-free languages by piecewise testable languages is decidable. This contrasts with the fact that testing if a context-free language is piecewise testable is undecidable. We generalize this decidability result by showing that, for every full trio (a class of languages that is closed under rather weak operations) which has decidable diagonal problem, separability with respect to piecewise testable languages is decidable. Examples of such classes are the languages defined by labeled vector addition systems and the languages accepted by higher order pushdown automata of order two. The proof goes through a result which is of independent interest and shows that, for any kind of languages I and E, separability can be decided by testing the existence of common patterns in I and E.
22 citations
TL;DR: The translation from protocols to pushdown automata is implemented, yielding the first tool that decides equivalence of (some class of) protocols, for an unbounded number of sessions, and it is shown that checking for equivalences of protocols is actually equivalent to checking for interchangeability of generalized, real-time deterministic push down automata.
Abstract: Formal methods have been very successful in analyzing security protocols for reachability properties such as secrecy or authentication. In contrast, there are very few results for equivalence-based properties, crucial for studying, for example, privacy-like properties such as anonymity or vote secrecy. We study the problem of checking equivalence of security protocols for an unbounded number of sessions. Since replication leads very quickly to undecidability (even in the simple case of secrecy), we focus on a limited fragment of protocols (standard primitives but pairs, one variable per protocol’s rules) for which the secrecy preservation problem is known to be decidable. Surprisingly, this fragment turns out to be undecidable for equivalence. Then, restricting our attention to deterministic protocols, we propose the first decidability result for checking equivalence of protocols for an unbounded number of sessions. This result is obtained through a characterization of equivalence of protocols in terms of equality of languages of (generalized, real-time) deterministic pushdown automata. We further show that checking for equivalence of protocols is actually equivalent to checking for equivalence of generalized, real-time deterministic pushdown automata. Very recently, the algorithm for checking for equivalence of deterministic pushdown automata has been implemented. We have implemented our translation from protocols to pushdown automata, yielding the first tool that decides equivalence of (some class of) protocols, for an unbounded number of sessions. As an application, we have analyzed some protocols of the literature including a simplified version of the basic access control (BAC) protocol used in biometric passports.
20 citations
Posted Content•
TL;DR: In this article, the authors explain how the connection between higher-order model checking and linear logic leads to a new and conceptually enlightening proof of the selection problem originally established by Carayol and Serre using collapsible pushdown automata.
Abstract: In this paper, we explain how the connection between higher-order model-checking and linear logic recently exhibited by the authors leads to a new and conceptually enlightening proof of the selection problem originally established by Carayol and Serre using collapsible pushdown automata. The main idea is to start from an infinitary and colored relational semantics of the lambdaY-calculus already formulated, and to replace it by its finitary counterpart based on finite prime-algebraic lattices. Given a higher-order recursion scheme G, the finiteness of its interpretation in the model enables us to associate to any MSO formula phi a new higher-order recursion scheme G_phi resolving the selection problem.
TL;DR: This paper demonstrates that the same worst-case 2 ?
Proceedings Article•
25 Jul 2015TL;DR: This paper introduces pushdown game structures over which ATL?
Abstract: In this paper we investigate the model-checking problem of pushdown multi-agent systems for ATL? specifications. To this aim, we introduce pushdown game structures over which ATL? formulas are interpreted. We show an algorithm that solves the addressed model-checking problem in 3EXPTIME. We also provide a 2EXPSPACE lower bound by showing a reduction from the word acceptance problem for deterministic Turing machines with doubly exponential space.
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TL;DR: The diagonal problem for higher-order pushdown automata (HOPDA), and hence the simultaneous unboundedness problem, is decidable and the downward closure of the set of words accepted by a given HOPDA is constructed.
Abstract: We show the diagonal problem for higher-order pushdown automata (HOPDA), and hence the simultaneous unboundedness problem, is decidable. From recent work by Zetzsche this means that we can construct the downward closure of the set of words accepted by a given HOPDA. This also means we can construct the downward closure of the Parikh image of a HOPDA. Both of these consequences play an important role in verifying concurrent higher-order programs expressed as HOPDA or safe higher-order recursion schemes.
12 Oct 2015
TL;DR: The authors define a new class of pushdown systems where the pushdown is a tree instead of a word and show that the resulting pushdown enjoys a decidable reachability problem, based on a preservation of recognizability result for the backward reachability relation.
Abstract: We define a new class of pushdown systems where the pushdown is a tree instead of a word. We allow a limited form of lookahead on the pushdown conforming to a certain ordering restriction, and we show that the resulting class enjoys a decidable reachability problem. This follows from a preservation of recognizability result for the backward reachability relation of such systems. As an application, we show that our simple model can encode several formalisms generalizing pushdown systems, such as ordered multi-pushdown systems, annotated higher-order pushdown systems, the Krivine machine, and ordered annotated multi-pushdown systems. In each case, our procedure yields tight complexity.
12 Oct 2015
TL;DR: This work presents coneqct: a contextual equivalence checking tool for terms of IMJ*, a fragment of Interface Middleweight Java for which the problem is decidable by reducing the equivalence problem to the emptiness problem for fresh-register pushdown automata.
Abstract: We present coneqct: a contextual equivalence checking tool for terms of IMJ*, a fragment of Interface Middleweight Java for which the problem is decidable. Given two, possibly open (containing free identifiers), terms of the language, the contextual equivalence problem asks if the terms can be distinguished by any possible IMJ context. Although there has been a lot of prior work describing methods for constructing proofs of equivalence by hand, ours is the first tool to decide equivalences for a non-trivial, object-oriented language, completely automatically. This is achieved by reducing the equivalence problem to the emptiness problem for fresh-register pushdown automata. An evaluation demonstrates that our tool works well on examples taken from the literature.
06 Jul 2015
TL;DR: In this article, the edit distance between two words is defined as the minimal number of word operations letter insertions, deletions, and substitutions necessary to transform a word from a regular language to a pushdown automaton.
Abstract: The edit distance between two words $$w_1, w_2$$ is the minimal number of word operations letter insertions, deletions, and substitutions necessary to transform $$w_1$$ to $$w_2$$. The edit distance generalizes to languages $$\mathcal {L}_1, \mathcal {L}_2$$, where the edit distance is the minimal number k such that for every word from $$\mathcal {L}_1$$ there exists a word in $$\mathcal {L}_2$$ with edit distance at most k. We study the edit distance computation problem between pushdown automata and their subclasses. The problem of computing edit distance to pushdown automata is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton the implementation, a standard model for programs with recursion to a regular language the specification. In this work, we present a complete picture of decidability and complexity for deciding whether, for a given threshold k, the edit distance from a pushdown automaton to a finite automaton is at most k.
24 Jan 2015
TL;DR: This model can overcome the reversibility restriction by exploiting the garbage tape to store popped symbols, and it is shown that the proposed model can simulate any quantum pushdown automaton with a classical stack as well as any probabilistic push down automaton.
Abstract: Several kinds of quantum pushdown automaton models have been proposed, and their computational power is investigated intensively However, for some quantum pushdown automaton models, it is not known whether quantum models are at least as powerful as classical counterparts or not This is due to the reversibility restriction In this paper, we introduce a new quantum pushdown automaton model that has a garbage tape This model can overcome the reversibility restriction by exploiting the garbage tape to store popped symbols We show that the proposed model can simulate any quantum pushdown automaton with a classical stack as well as any probabilistic pushdown automaton We also show that our model can solve a certain promise problem exactly while deterministic pushdown automata cannot These results imply that our model is strictly more powerful than classical counterparts in the setting of exact, one-sided error and non-deterministic computation
06 Jul 2015
TL;DR: A construction of Cook 1971 is applied to show that the intersection non-emptiness problem for one PDA pushdown automaton and a finite list of DFA's deterministic finite automata characterizes the complexity class P, and constants c_1 and c_2 are shown to be solvable in time.
Abstract: We apply a construction of Cook 1971 to show that the intersection non-emptiness problem for one PDA pushdown automaton and a finite list of DFA's deterministic finite automata characterizes the complexity class P. In particular, we show that there exist constants $$c_1$$ and $$c_2$$ such that for every k, intersection non-emptiness for one PDA and k DFA's is solvable in $$On^{c_1 k}$$ time, but is not solvable in $$On^{c_2 k}$$ time. Then, for every k, we reduce intersection non-emptiness for one PDA and $$2^k$$ DFA's to non-emptiness for multi-stack pushdown automata with k-phase switches to obtain a tight time complexity lower bound. Further, we revisit a construction of Veanes 1997 to show that the intersection non-emptiness problem for tree automata also characterizes the complexity class P. We show that there exist constants $$c_1$$ and $$c_2$$ such that for every k, intersection non-emptiness for k tree automata is solvable in $$On^{c_1 k}$$ time, but is not solvable in $$On^{c_2 k}$$ time.
18 Aug 2015
TL;DR: One-way quantum one-counter automaton with zero-error is more powerful than its probabilistic counterpart on promise problems and it is shown that one-way Probabilistic one blind- counter automata cannot recognize Kleene closure of equality language.
Abstract: In this paper, we show that one-way quantum one-counter automaton with zero-error is more powerful than its probabilistic counterpart on promise problems. Then, we obtain a similar separation result between Las Vegas one-way probabilistic one-counter automaton and one-way deterministic one-counter automaton. Lastly, it was conjectured that one-way probabilistic one blind-counter automata cannot recognize Kleene closure of equality language [A. Yakaryilmaz: Superiority of one-way and realtime quantum machines. RAIRO - Theor. Inf. and Applic. 46(4): 615–641 (2012)]. We show that this conjecture is false.
TL;DR: The characterization of algebraic concepts such as subautomaton, retrievability and connectivity of a fuzzy automaton in terms of its layers, and to associate upper semilattices with fuzzy automata are characterized.
Abstract: This paper is towards the characterization of algebraic concepts such as subautomaton, retrievability and connectivity of a fuzzy automaton in terms of its layers, and to associate upper semilattices with fuzzy automata. Meanwhile, we provide a decomposition of a fuzzy automaton in terms of its layers and propose a construction of a fuzzy automaton corresponding to a given finite partially ordered set (poset). Finally, we establish an isomorphism between the poset of class of subautomata of a fuzzy automaton and an upper semilattice.
13 Jul 2015
TL;DR: A quantitative logic on timed words which is expressively equivalent to timed pushdown automata is introduced, an extension of Wilke’s relative distance logic by quantitative matchings.
Abstract: Dense-timed pushdown automata with a timed stack were introduced by Abdulla et al. in LICS 2012 to model the behavior of real-time recursive systems. In this paper, we introduce a quantitative logic on timed words which is expressively equivalent to timed pushdown automata. This logic is an extension of Wilke’s relative distance logic by quantitative matchings. To show the expressive equivalence result, we prove a decomposition theorem which establishes a connection between timed pushdown languages and visibly pushdown languages of Alur and Mudhusudan; then we apply their result about the logical characterization of visibly pushdown languages. As a consequence, we obtain the decidability of the satisfiability problem for our new logic.
09 Sep 2015
TL;DR: In input-driven pushdown automata (\(\text {IDPDA}\)) the input alphabet is divided into three distinct classes and the actions on the pushdown store are solely governed by the input symbols, which is extended in such a way that the input is preprocessed by a deterministic sequential transducer.
Abstract: 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 transducer. These automata are called tinput-driven pushdown automata (\(\text {TDPDA}\)) and it turns out that \(\text {TDPDA}\)s are more powerful than \(\text {IDPDA}\)s but still not as powerful as real-time deterministic pushdown automata. Nevertheless, even this stronger model has still good closure and decidability properties. In detail, it is shown that \(\text {TDPDA}\)s are closed under the Boolean operations union, intersection, and complementation. Furthermore, decidability procedures for the inclusion problem as well as for the questions of whether a given automaton is a \(\text {TDPDA}\) or an \(\text {IDPDA}\) are developed. Finally, representation theorems for the context-free languages using \(\text {IDPDA}\)s and \(\text {TDPDA}\)s are established.
Proceedings Article•
11 Dec 2015TL;DR: A framework of reservoir computing that is capable of both connectionist machine intelligence and symbolic computation that corresponds to a binary valued and nonlinear neuro-symbolic architecture is introduced.
Abstract: In this paper, we introduce a framework of reservoir computing that is capable of both connectionist machine intelligence and symbolic computation Cellular automaton is used as the reservoir of dynamical systems A cellular automaton is a very sparsely connected network with logical nodes and nonlinear/logical connection functions, hence the proposed system corresponds to a binary valued and nonlinear neuro-symbolic architecture Input is randomly projected onto the initial conditions of automaton cells and nonlinear computation is performed on the input via application of a rule in the automaton for a period of time The evolution of the automaton creates a space-time volume of the automaton state space, and it is used as the reservoir In addition to being used as the feature representation for pattern recognition, binary reservoir vectors can be combined using Boolean operations as in hyperdimensional computing, paving a direct way symbolic processing To demonstrate the capability of the proposed system, we make analogies directly on image data by asking 'What is the Automobile of Air'?, and make logical inference using rules by asking 'Which object is the largest?'
TL;DR: This paper proposed a method for testing the directability of a fuzzy automaton using the mergeability relation, which takes each state of a fuzzy automaton to a single state with some membership value.
Abstract: The aim of this paper is testing the directability of a given fuzzy automaton. A fuzzy automaton is directable if there exists a word, a directing word, which takes each state of a fuzzy automaton to a single state with some membership value. In this paper, we proposed a method for testing the directability of a fuzzy automaton using the mergeability relation.
TL;DR: The proposed process is that anchor seed (AS) will be selected from given data set of nucleotide base pairs for local sequence alignment and quick splitting techniques will separate the AS from all the DNA genome segments.
Abstract: Space complexity is a million dollar question in DNA sequence alignments In this regard, memory saving under pushdown automata can help to reduce the occupied spaces in computer memory Our proposed process is that anchor seed (AS) will be selected from given data set of nucleotide base pairs for local sequence alignment Quick splitting techniques will separate the AS from all the DNA genome segments Selected AS will be placed to pushdown automata’s (PDA) input unit Whole DNA genome segments will be placed into PDA’s stack AS from input unit will be matched with the DNA genome segments from stack of PDA
Match, mismatch and indel of nucleotides will be popped from the stack under the control unit of pushdown automata During the POP operation on stack, it will free the memory cell occupied by the nucleotide base pair
01 Jan 2015
TL;DR: A decomposition theorem is proved which establishes a connection between weighted timed push down languages and visibly pushdown languages of Alur and Mudhusudan and introduces a weighted MSO logic on timed words which is expressively equivalent to weighted timing pushdown automata.
Abstract: Weighted dense-timed pushdown automata with a timed stack were introduced by Abdulla, Atig and Stenman to model the behavior of real-time recursive systems. Motivated by the decidability of the optimal reachability problem for weighted timed pushdown automata and weighted logic of Droste and Gastin, we introduce a weighted MSO logic on timed words which is expressively equivalent to weighted timed pushdown automata. To show the expressive equivalence result, we prove a decomposition theorem which establishes a connection between weighted timed pushdown languages and visibly pushdown languages of Alur and Mudhusudan; then we apply their result about the logical characterization of visibly pushdown languages.
01 Jan 2015
TL;DR: The main result states that the support of a weighted unranked tree automaton over a zero-sum free, commutative strong bimonoid is recognizing and derived analogous results for the supports of nested weighted automata are derived.
Abstract: We investigate the supports of weighted unranked tree automata. Our main result states that the support of a weighted unranked tree automaton over a zero-sum free, commutative strong bimonoid is recognizable. For this, we use methods of Kirsten (DLT 2009), in particular, his construction of finite automata recognizing the supports of weighted automata on strings over zero-sum free, commutative semirings. We also get an effective construction of a finite tree automaton recognizing the support of a given weighted unranked tree automaton for zero-sum free, commutative strong bimonoids where Kirsten's zero generation problem is decidable. In addition, we give a translation of nested weighted automata into weighted unranked tree automata for arbitrary commutative strong bimonoids. As a consequence, we derive analogous results for the supports of nested weighted automata. Finally, we give similar results for the supports of weighted pushdown automata.
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TL;DR: Visibly Linear Dynamic Logic (VLDL) as mentioned in this paper extends LTL by temporal operators that are guarded by visibly pushdown languages over finite words, which can express recursive properties of programs with unbounded call stacks.
Abstract: We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown languages over finite words. In VLDL one can, e.g., express that a function resets a variable to its original value after its execution, even in the presence of an unbounded number of intermediate recursive calls. We prove that VLDL describes exactly the $\omega$-visibly pushdown languages. Thus it is strictly more expressive than LTL and able to express recursive properties of programs with unbounded call stacks.
The main technical contribution of this work is a translation of VLDL into $\omega$-visibly pushdown automata of exponential size via one-way alternating jumping automata. This translation yields exponential-time algorithms for satisfiability, validity, and model checking. We also show that visibly pushdown games with VLDL winning conditions are solvable in triply-exponential time. We prove all these problems to be complete for their respective complexity classes.