Pushdown automaton

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

Algorithms for guided tree automata

Abstract: When reading an input tree, a bottom-up tree automaton is unaware of where it is relative to the root. This problem is important to the efficient implementation of decision procedures for the Monadic Second-order Logic (M2L) on finite trees. In [KS97], it is shown how exponential state space blow-ups may occur in common situations. The analysis of the problem leads to the notion of guided tree automaton for combatting such explosions. The guided automaton is equipped with separate state spaces that are assigned by a top-down automaton, called the guide. In this paper, we explore the algorithmic and practical problems arising from this relatively complicated automaton concept. Our solutions are based on a BDD representation of automata [HJJ + 96], which allows the practical handling of automata on very large alphabets. In addition, we propose data structures for avoiding the quadratic size of transition tables associated with tree automata. We formulate and analyze product, projection (subset construction), and minimization algorithms for guided tree automata. We show that our product algorithm for certain languages are asymptotically faster than the usual algorithm that relies on transition tables. Also, we provide some preliminary experimental results on the use of guided automata vs. standard tree automata.

Truly on-the-fly LTL model checking

Abstract: We propose a novel algorithm for automata-based LTL model checking that interleaves the construction of the generalized Buchi automaton for the negation of the formula and the emptiness check. Our algorithm first converts the LTL formula into a linear weak alternating automaton; configurations of the alternating automaton correspond to the locations of a generalized Buchi automaton, and a variant of Tarjan's algorithm is used to decide the existence of an accepting run of the product of the transition system and the automaton. Because we avoid an explicit construction of the Buchi automaton, our approach can yield significant improvements in runtime and memory, for large LTL formulas. The algorithm has been implemented within the Spin model checker, and we present experimental results for some benchmark examples.

Games with winning conditions of high Borel complexity

Abstract: We first consider infinite two-player games on pushdown graphs. In previous work, Cachat et al. [Solving pushdown games with a Σ3-winning condition, in: Proc. 11th Annu. Conf. of the European Association for Computer Science Logic, CSL 2002, Lecture Notes in Computer Science, Vol. 2471, Springer, Berlin, 2002, pp. 322-336] have presented a winning decidable condition that is Σ3-complete in the Borel hierarchy. This was the first example of a decidable winning condition of such Borel complexity. We extend this result by giving a family of decidable winning conditions of arbitrary finite Borel complexity. From this family, we deduce a family of decidable winning conditions of arbitrary finite Borel complexity for games played on finite graphs. The problem of deciding the winner for these conditions is shown to be non-elementary.

Time and tape bounded auxiliary pushdown automata

Abstract: We consider language families defined by nondeterministic and deterministic log(n)-tape bounded auxiliary pushdown automata within polynomial time. It is known that these families are precisely the set of languages which are (many-one) log tape reducible to context-free languages and deterministic context-free languages, respectively. The results described here relate questions concerning these classes to other complexity classes and to questions concerning the tape complexity of context-free languages, resolution based proof procedures, solvable path systems, and deterministic context-free languages.