8,853 research outputs found
On the Complexity of the Equivalence Problem for Probabilistic Automata
Checking two probabilistic automata for equivalence has been shown to be a
key problem for efficiently establishing various behavioural and anonymity
properties of probabilistic systems. In recent experiments a randomised
equivalence test based on polynomial identity testing outperformed
deterministic algorithms. In this paper we show that polynomial identity
testing yields efficient algorithms for various generalisations of the
equivalence problem. First, we provide a randomized NC procedure that also
outputs a counterexample trace in case of inequivalence. Second, we show how to
check for equivalence two probabilistic automata with (cumulative) rewards. Our
algorithm runs in deterministic polynomial time, if the number of reward
counters is fixed. Finally we show that the equivalence problem for
probabilistic visibly pushdown automata is logspace equivalent to the
Arithmetic Circuit Identity Testing problem, which is to decide whether a
polynomial represented by an arithmetic circuit is identically zero.Comment: technical report for a FoSSaCS'12 pape
Equivalence of Deterministic One-Counter Automata is NL-complete
We prove that language equivalence of deterministic one-counter automata is
NL-complete. This improves the superpolynomial time complexity upper bound
shown by Valiant and Paterson in 1975. Our main contribution is to prove that
two deterministic one-counter automata are inequivalent if and only if they can
be distinguished by a word of length polynomial in the size of the two input
automata
Regular Boardgames
We propose a new General Game Playing (GGP) language called Regular
Boardgames (RBG), which is based on the theory of regular languages. The
objective of RBG is to join key properties as expressiveness, efficiency, and
naturalness of the description in one GGP formalism, compensating certain
drawbacks of the existing languages. This often makes RBG more suitable for
various research and practical developments in GGP. While dedicated mostly for
describing board games, RBG is universal for the class of all finite
deterministic turn-based games with perfect information. We establish
foundations of RBG, and analyze it theoretically and experimentally, focusing
on the efficiency of reasoning. Regular Boardgames is the first GGP language
that allows efficient encoding and playing games with complex rules and with
large branching factor (e.g.\ amazons, arimaa, large chess variants, go,
international checkers, paper soccer).Comment: AAAI 201
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