We describe an automata-theoretic approach to the automatic verification of finite-state programs. The basic idea underlying this approach is that for any temporal formula we can construct an alternating automaton that accepts precisely the computations that satisfy the formula. For linear temporal logics the automaton runs on infinite words while for branching temporal logics the automaton run...

We describe an efficient implementation of a CTL model-checking algorithm based on alternating automata. We use this to check properties of an asynchronous micropipeline design described in the Rainbow framework, which operates at the micropipeline level and leads to compact models of the hardware. We also use alternating automata to characterise the expressive power and model-checking complexi...

We show that the family of tree languages recognized by weak alternating automata is closed by three set theoretic operations that correspond to sum, multiplication by ordinals < ω, and pseudoexponentiation with the base ω1 of the Wadge degrees. In consequence, the Wadge hierarchy of weakly recognizable tree languages has the height of at least ε0, that is the least fixed point of the exponenti...

In this article we consider two-way two-tape (alternating) automata accepting pairs of words and we study some closure properties of this model. Our main result is that such alternating automata are not closed under complementation for non-unary alphabets. This improves a similar result of Kari and Moore for picture languages. We also show that these deterministic, non-deterministic and alterna...

We prove Cardy’s formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular automaton corresponds to the zero-temperature case of Domany’s stochastic Ising ferromagnet on the hexagonal lattice H (with alternating updates of two sublattices) [7]; it may also be realized on the tr...

Model checking of LTL formulæ is traditionally carried out by a conversion to Büchi automata, and there is therefore a large body of research in this area including some recent studies on the use of alternating automata as an intermediate representation. Bounded model checking has until recently been apart from this, typically using a direct conversion from LTL to propositional logic. In this p...

In this paper, we extend the notion of (word) derivatives and partial due to (respectively) Brzozowski Antimirov tree using already known inductive formulae quotients. We define a new family extended regular expressions (using negation or intersection operators), show how compute Brzozowski-like automaton; fixed point construction, when it exists, is derivative automaton. Such deterministic aut...

A deterministic pushdown automaton (dpda) is described as finite-turn if there is a bound on the number of times the direction of the stack movement can change in the set of all derivations from the starting configuration. The purpose of this paper is to show that there exists a procedure for deciding whether two such finite-turn machines recognize the same language. By virtue of a direct corre...

In this paper, we present some connections between tree automaton theory and hyperstructure theory. In this regard, at first we construct some hyperoperations on the set of trees and, specially, prove that one of them creates a join space. Also, we define a hyperoperation on the states of a tree automaton and, based on the properties of the tree automaton, we show that the proposed hyperoperati...

The last theorem of Lecture 9 assures us that in any Büchi game one of the two players has a positional winning strategy. Thus, for any alternating Büchi automaton (ABA ) A and word w, either the automaton or the pathfinder has a positional winning strategy in the game G(A,w). Thus, if A accepts w there is a positional run for A on w. Consider the ABA A1 from the previous lecture. Here is a pos...