Multi-Push-Down Languages and Grammars

Breveglieri, Luca; Cherubini, Alessandra; Citrini, Claudio; Reghizzi, Stefano Crespi

doi:10.1142/s0129054196000191

Cited by 84 publications

(75 citation statements)

References 6 publications

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“…The proof makes use of the ideas from [3], where a proof for a normal form for D n -grammars (see below) is given. Notice, however, that we do not use the same normal form as the one of [3] for MPDA.…”

Section: -Only the Following Transitions Are Allowedmentioning

confidence: 99%

“…To retain desirable decidability properties of pushdown automata, such as emptiness, one needs to restrict the model accordingly. In [3], Breveglieri et al define multi-pushdown automata (MPDA), which impose a linear ordering on stacks. Stack operations are henceforth constrained in such a way that a pop operation is reserved to the first non-empty stack.…”

Section: Introductionmentioning

confidence: 99%

“…Recall that 2ETIME is the class of all decision problems solvable by a deterministic Turing machine in time 2 2 dn for some constant d. In proving the upper bound, we correct an error in the decidability proof given in [3]. 3 We keep their main idea: MPDA are reduced to equivalent depthn-grammars. Deciding emptiness for these grammars then amounts to checking emptiness of an ordinary context-free grammar.…”

Section: Introductionmentioning

confidence: 99%

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Emptiness of Multi-pushdown Automata Is 2ETIME-Complete

Atig

Bollig

Habermehl

2008

Developments in Language Theory

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Abstract. We consider multi-pushdown automata, a multi-stack extension of pushdown automata that comes with a constraint on stack operations: a pop can only be performed on the first non-empty stack (which implies that we assume a linear ordering on the collection of stacks). We show that the emptiness problem for multi-pushdown automata is 2ETIME-complete wrt. the number of stacks. Containment in 2ETIME is shown by translating an automaton into a grammar for which we can check if the generated language is empty. The lower bound is established by simulating the behavior of an alternating Turing machine working in exponential space. We also compare multi-pushdown automata with the model of bounded-phase multi-stack (visibly) pushdown automata.

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Section: -Only the Following Transitions Are Allowedmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Emptiness of Multi-pushdown Automata Is 2ETIME-Complete

Atig

Bollig

Habermehl

2008

Developments in Language Theory

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“…Lemma 3.5 ( [BCCC96]). If M 1 and M 2 are two n-OMPAs over an alphabet Σ, then it is possible to construct an n-OMPA M over Σ such that:…”

Section: Ordered Multi-pushdown Automatamentioning

confidence: 99%

“…In [BCCC96], Breveglieri et al define ordered multi-pushdown automata (OMPA), which impose a linear ordering on stacks. Stack transitions are constrained in such a way that a pop transition is reserved to the first non-empty stack.…”

Section: Introductionmentioning

confidence: 99%

Model-Checking of Ordered Multi-Pushdown Automata

Atig¹

2012

Logical Methods in Computer Science

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Abstract. We address the verification problem of ordered multi-pushdown automata: A multi-stack extension of pushdown automata that comes with a constraint on stack transitions such that a pop can only be performed on the first non-empty stack. First, we show that the emptiness problem for ordered multi-pushdown automata is in 2ETIME. Then, we prove that, for an ordered multi-pushdown automata, the set of all predecessors of a regular set of configurations is an effectively constructible regular set. We exploit this result to solve the global model-checking which consists in computing the set of all configurations of an ordered multi-pushdown automaton that satisfy a given w-regular property (expressible in linear-time temporal logics or the linear-time µ-calculus). As an immediate consequence, we obtain an 2ETIME upper bound for the model-checking problem of w-regular properties for ordered multi-pushdown automata (matching its lowerbound).

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Some Decision Problems Concerning Semilinearity and Commutation

Harju

Ibarra

Karhumäki

et al. 2002

Journal of Computer and System Sciences

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Let M be a class of automata (in a precise sense to be defined) and M c the class obtained by augmenting each automaton in M with finitely many reversal-bounded counters. We show that if the languages defined by M are effectively semilinear, then so are the languages defined by M c , and, hence, their emptiness problem is decidable. We give examples of how this result can be used to show the decidability of certain problems concerning the equivalence of morphisms on languages. We also prove a surprising undecidability result for commutation of languages: given a fixed two-element code K, it is undecidable whether a given context-free language L commutes with K, i.e., LK ¼ KL. # 2002 Elsevier Science (USA)

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Multi-Push-Down Languages and Grammars

Cited by 84 publications

References 6 publications

Emptiness of Multi-pushdown Automata Is 2ETIME-Complete

Emptiness of Multi-pushdown Automata Is 2ETIME-Complete

Model-Checking of Ordered Multi-Pushdown Automata

Some Decision Problems Concerning Semilinearity and Commutation

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