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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 for every n , there is a language which is accepted by an n -state nondeterministic one-way finite automaton, yet which is not accepted by any sweeping automaton with fewer than 2 n states.
88 citations
TL;DR: It is shown that finite unions of congruence classes of canonical monadic tree rewriting systems can be recognized by deterministic tree pushdown automata without the additional acceptance conditions used in op. cit .
86 citations
16 Dec 2004
TL;DR: The class of visibly pushdown languages has been recently defined as a subclass of context-free languages with desirable closure properties and tractable decision problems and it is established that, unlike pushdown games with pushdown winning conditions, visibly push down games are decidable and are 2Exptime-complete.
Abstract: The class of visibly pushdown languages has been recently defined as a subclass of context-free languages with desirable closure properties and tractable decision problems. We study visibly pushdown games, which are games played on visibly pushdown systems where the winning condition is given by a visibly pushdown language. We establish that, unlike pushdown games with pushdown winning conditions, visibly pushdown games are decidable and are 2Exptime-complete. We also show that pushdown games against Ltl specifications and Caret specifications are 3Exptime-complete. Finally, we establish the topological complexity of visibly pushdown languages by showing that they are a subclass of Boolean combinations of Σ3 sets. This leads to an alternative proof that visibly pushdown automata are not determinizable and also shows that visibly pushdown games are determined.
86 citations
TL;DR: It is shown that the problem of solving parity games over the configuration graphs of order-n CPDA is n-EXPTIME complete, subsuming several well-known results about the solvability of games over higher-order pushdown graphs by (respectively) Walukiewicz, Cachat, and Knapik et al.
Abstract: We consider recursion schemes (not assumed to be homogeneously typed, and hence not necessarily safe) and use them as generators of (possibly infinite) ranked trees. A recursion scheme is essentially a finite typed deterministic term rewriting system that generates, when one applies the rewriting rules ad infinitum, an infinite tree, called its value tree. A fundamental question is to provide an equivalent description of the trees generated by recursion schemes by a class of machines. In this article, we answer this open question by introducing collapsible pushdown automata (CPDA), which are an extension of deterministic (higher-order) pushdown automata. A CPDA generates a tree as follows. One considers its transition graph, unfolds it, and contracts its silent transitions, which leads to an infinite tree, which is finally node labelled thanks to a map from the set of control states of the CPDA to a ranked alphabet. Our contribution is to prove that these two models, higher-order recursion schemes and collapsible pushdown automata, are equi-expressive for generating infinite ranked trees. This is achieved by giving effective transformations in both directions.
86 citations
26 Jun 2005
TL;DR: This paper focuses on computing the expected values and variances of various random variables defined over runs of a given probabilistic pushdown automaton, and shows how to compute the expected accumulated reward and the expected gain for certain classes of reward functions.
Abstract: Probabilistic pushdown automata (pPDA) have been identified as a natural model for probabilistic programs with recursive procedure calls. Previous works considered the decidability and complexity of the model-checking problem for pPDA and various probabilistic temporal logics. In this paper we concentrate on computing the expected values and variances of various random variables defined over runs of a given probabilistic pushdown automaton. In particular, we show how to compute the expected accumulated reward and the expected gain for certain classes of reward functions. Using these results, we show how to analyze various quantitative properties of pPDA that are not expressible in conventional probabilistic temporal logics.
84 citations