Pushdown automaton

About: Pushdown automaton is a research topic. Over the lifetime, 1868 publications have been published within this topic receiving 35399 citations.

On the Complexity of Equivalence and Minimisation for Q-weighted Automata

Abstract: This paper is concerned with the computational complexity of equivalence and minimisation for automata with transition weights in the field Q of rational numbers. We use polynomial identity testing and the Isolation Lemma to obtain complexity bounds, focussing on the class NC of problems within P solvable in polylogarithmic parallel time. For finite Q-weighted automata, we give a randomised NC procedure that either outputs that two automata are equivalent or returns a word on which they differ. We also give an NC procedure for deciding whether a given automaton is minimal, as well as a randomised NC procedure that minimises an automaton. We consider probabilistic automata with rewards, similar to Markov Decision Processes. For these automata we consider two notions of equivalence: expectation equivalence and distribution equivalence. The former requires that two automata have the same expected reward on each input word, while the latter requires that each input word induce the same distribution on rewards in each automaton. For both notions we give algorithms for deciding equivalence by reduction to equivalence of Q-weighted automata. Finally we show that the equivalence problem for Q-weighted visibly pushdown automata is logspace equivalent to the polynomial identity testing problem.

The Complexity of Games on Higher Order Pushdown Automata

Abstract: We prove an n-EXPTIME lower bound for the problem of deciding the winner in a reachability game on Higher Order Pushdown Automata (HPDA) of level n This bound matches the known upper bound for parity games on HPDA As a consequence the mu-calculus model checking over graphs given by n-HPDA is n-EXPTIME complete

Two applications of complementation via inductive counting

Abstract: A recent proof that nondeterministic space-bounded complexity classes are closed under complementation is used to develop two further applications of the inductive counting technique. An errorless probabilistic algorithm is given for the undirected graph s-t connectivity problem that runs in O(log n) space and polynomial expected time, and it is shown that the class LOGCFL is closed under complementation. The latter is a special case of a general result that shows closure under complementation of classes defined by semiunbounded fan-in circuits (or, equivalently, nondeterministic auxiliary pushdown automata or tree-sized bounded alternating Turing machines). As one consequence, small numbers of role switches in two-person pebbling can be eliminated. >

Synchronization of pushdown automata

Abstract: We introduce the synchronization of a pushdown automaton by a sequential transducer associating an integer to each input word. The visibly pushdown automata are the automata synchronized by an one state transducer whose output labels are –1,0,1. For each transducer, we can decide whether a pushdown automaton is synchronized. The pushdown automata synchronized by a given transducer accept languages which form an effective boolean algebra containing the regular languages and included in the deterministic real-time context-free languages.