Topic
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: In this article, the model checking problem for probabilistic pushdown automata (pPDA) and properties expressible in various Proto-Probabilistic logics is studied.
Abstract: We consider the model checking problem for probabilistic
pushdown automata (pPDA) and properties expressible in various
probabilistic logics. We start with properties that can be
formulated as instances of a generalized random walk problem.
We prove that both qualitative and quantitative model checking
for this class of properties and pPDA is decidable. Then we
show that model checking for the qualitative fragment of the
logic PCTL and pPDA is also decidable. Moreover, we develop an
error-tolerant model checking algorithm for PCTL and the
subclass of stateless pPDA. Finally, we consider the class of
omega-regular properties and show that both qualitative and
quantitative model checking for pPDA is decidable.
114 citations
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15 Dec 2003TL;DR: Two equivalent characterizations of the Caucal hierarchy are given, one of which replaces the language-theoretic operation of a rational mapping by an MSO-transduction and the unfolding by the treegraph operation and the second is non-iterative.
Abstract: In this paper we give two equivalent characterizations of the Caucal hierarchy, a hierarchy of infinite graphs with a decidable monadic second-order (MSO) theory. It is obtained by iterating the graph transformations of unfolding and inverse rational mapping. The first characterization sticks to this hierarchical approach, replacing the language-theoretic operation of a rational mapping by an MSO-transduction and the unfolding by the treegraph operation. The second characterization is non-iterative. We show that the family of graphs of the Caucal hierarchy coincides with the family of graphs obtained as the e-closure of configuration graphs of higher-order pushdown automata.
114 citations
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TL;DR: A new procedure for inferring the structure of a finitestate automaton (FSA) from its input/output behavior, using access to the automaton to perform experiments, based on the notion of equivalence between testa.
Abstract: We present new procedures for inferring the structure of a finite-state automaton (FSA) from its input/output behavior, using access to the automaton to perform experiments.Our procedures use a new representation for finite automata, based on the notion of equivalence between tests. We call the number of such equivalence classes the diversity of the automaton; the diversity may be as small as the logarithm of the number of states of the automaton. For the special class of permutation automata, we describe an inference procedure that runs in time polynomial in the diversity and log(1/d), where d is a given upper bound on the probability that our procedure returns an incorrect result. (Since our procedure uses randomization to perform experiments, there is a certain controllable chance that it will return an erroneous result.) We also discuss techniques for handling more general automata.We present evidence for the practical efficiency of our approach. For example, our procedure is able to infer the structure of an automaton based on Rubik's Cube (which has approximately 1019 states) in about 2 minutes on a DEC MicroVax. This automaton is many orders of magnitude larger than possible with previous techniques, which would require time proportional at least to the number of global states. (Note that in this example, only a small fraction (10-14) of the global states were even visited.)Finally, we present a new procedure for inferring automata of a special type in which the global state is composed of a vector of binary local state variables, all of which are observable (or visible) to the experimenter. Our inference procedure runs provably in time polynomial in the size of this vector (which happens to be the diversity of the automaton), even though the global state space may be exponentially larger. The procedure plans and executes experiments on the unknown automaton; we show that the number of input symbols given to the automaton during this process is (to within a constant factor) the best possible.
113 citations
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16 Dec 2004TL;DR: This paper surveys recent work conducted by the authors together with colleagues on he algorithmic verification of probabilistic procedural programs ([BKS,EKM04,EY04]; a very rich theory emerges for these models.
Abstract: Monolithic finite-state probabilistic programs have been abstractly modeled by finite Markov chains, and the algorithmic verification problems for them have been investigated very extensively. In this paper we survey recent work conducted by the authors together with colleagues on he algorithmic verification of probabilistic procedural programs ([BKS,EKM04,EY04]). Probabilistic procedural programs can more naturally be modeled by recursive Markov chains ([EY04)], or equivalently, probabilistic pushdown automata ([EKM04)]. A very rich theory emerges for these models. While our recent work solves a number of verification problems for these models, many intriguing questions remain open.
111 citations
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TL;DR: The question of whether there is a deterministic counterpart to the notion of a fuzzy automaton is considered and a definition of deterministic fuzzy automata is proposed and it is shown that they are equally powerful as fuzzyAutomata.
106 citations