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Pushdown automaton
About: Pushdown automaton is a research topic. Over the lifetime, 1868 publications have been published within this topic receiving 35399 citations.
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TL;DR: It is shown that pPDA language equivalence (and hence multiplicity equivalence of context-free grammars) is in PSPACE and at least as hard as the polynomial identity testing problem.
Abstract: We study the language equivalence problem for probabilistic pushdown automata (pPDA) and their subclasses. We show that the problem is interreducible with the multiplicity equivalence problem for context-free grammars, the decidability of which has been open for several decades. Interreducibility also holds for pPDA with one control state. In contrast, for the case of a one-letter input alphabet we show that pPDA language equivalence (and hence multiplicity equivalence of context-free grammars) is in PSPACE and at least as hard as the polynomial identity testing problem.
14 citations
TL;DR: The generalized procedure is shown to yield an equivalence test for proper dpdas, and it is shown that the equivalence problem for proper automata is reducible to the problem of deodmg whether or not an automaton ~s proper.
Abstract: A generalizauon of the alternate stacking procedure of Valiant for decidmg the eqmvalence of some determuusuc pushdown automata (dpda) Is introduced. To analyze the power of the generalized procedure, a subclass of dpdas, called the proper dpdas, is defined. This class properly contains the nonsingular dpdas and the real-time strict dpdas, and the corresponding class of languages properly contains the real-tune strict determmlsttc languages. The generalized procedure is shown to yield an equivalence test for proper dpdas, at least one of which ~s also a fuute-turn machine. It is also shown that the equivalence problem for proper automata is reducible to the problem of deodmg whether or not an automaton ~s proper.
13 citations
25 Jan 2014
TL;DR: The notion of many-one CFL-reducibility was introduced in this article, where the CFL hierarchy is shown to have an upward collapse property with respect to the first and second levels of the hierarchy.
Abstract: We implement various oracle mechanisms on nondeterministic pushdown automata, which naturally induce nondeterministic reducibilities among formal languages in a theory of context-free languages. In particular, we examine a notion of nondeterministic many-one CFL-reducibility and carry out ground work of formulating a coherent framework for further expositions. Another more powerful reducibility—Turing CFL-reducibility—is also discussed in comparison. The Turing CFL-reducibility, in particular, makes it possible to induce a useful hierarchy (the CFL hierarchy) built over the family CFL of context-free languages. For each level of this hierarchy, basic structural properties are proven and three alternative characterizations are presented. We also show that the CFL hierarchy enjoys an upward collapse property. The first and second levels of the hierarchy are proven to be different. We argue that the CFL hierarchy coincides with a hierarchy over CFL built by applications of many-one CFL-reductions. Our goal is to provide a solid foundation for structural-complexity analyses in automata theory.
13 citations
01 Jan 2009
TL;DR: It is shown that the winner in infinite-state stochastic games generated by stateless pushdown automata can be determined in $\textbf {NP} \cap \textbf{co-NP}$.
Abstract: We consider a class of infinite-state stochastic games generated by stateless pushdown automata (or, equivalently, 1-exit recursive state machines), where the winning objective is specified by a regular set of target configurations and a qualitative probability constraint `${>}0$' or `${=}1$'. The goal of one player is to maximize the probability of reaching the target set so that the constraint is satisfied, while the other player aims at the opposite. We show that the winner in such games can be determined in $\textbf{NP} \cap \textbf{co-NP}$. Further, we prove that the winning regions for both players are regular, and we design algorithms which compute the associated finite-state automata. Finally, we show that winning strategies can be synthesized effectively.
13 citations
14 Mar 2016
TL;DR: Dense-time visibly pushdown automata that make both the call-return as well as resets visible are introduced and MSO logic characterization is presented and the decidability of the emptiness problem for these automata is proved, paving way for verification problem for dense-timed pushdown Automata specification.
Abstract: Two of the most celebrated results that effectively exploit visual representation to give logical characterization and decidable model-checking include visibly pushdown automata (VPA) by Alur and Madhusudan and event-clock automata (ECA) by Alur, Fix and Henzinger. VPA and ECA—by making the call-return edges visible and by making the clock-reset operation visible, respectively—recover decidability for the verification problem for pushdown automata implementation against visibly pushdown automata specification and timed automata implementation against event-clock timed automata specification, respectively. In this work we combine and extend these two works to introduce dense-time visibly pushdown automata that make both the call-return as well as resets visible. We present MSO logic characterization of these automata and prove the decidability of the emptiness problem for these automata paving way for verification problem for dense-timed pushdown automata against dense-timed visibly pushdown automata specification.
13 citations