Silent Transitions in Automata with Storage

We consider the computational power of silent transitions in one-way automata with storage. Specifically, we ask which storage mechanisms admit a transformation of a given automaton into one that accepts the same language and reads at least one input symbol in each step. We study this question using the model of valence automata. Here, a finite automaton is equipped with a storage mechanism that is given by a monoid. This work presents generalizations of known results on silent transitions. For two classes of monoids, it provides characterizations of those monoids that allow the removal of \lambda-transitions. Both classes are defined by graph products of copies of the bicyclic monoid and the group of integers. The first class contains pushdown storages as well as the blind counters while the second class contains the blind and the partially blind counters.Comment: 32 pages, submitte

Some perspectives of infinite-state verification

Abstract. We report on recent progress in the study of infinite transition systems for which interesting properties (like reachability of designated states) can be checked algorithmically. Two methods for the generation of such models are discussed: the construction from simpler models via operations like unfolding and synchronized product, and the internal representation of state spaces by regular sets of words or trees.

Quantitative languages defined by functional automata

A weighted automaton is functional if any two accepting runs on the same finite word have the same value. In this paper, we investigate functional weighted automata for four different measures: the sum, the mean, the discounted sum of weights along edges and the ratio between rewards and costs. On the positive side, we show that functionality is decidable for the four measures. Furthermore, the existential and universal threshold problems, the language inclusion problem and the equivalence problem are all decidable when the weighted automata are functional. On the negative side, we also study the quantitative extension of the realizability problem and show that it is undecidable for sum, mean and ratio. We finally show how to decide whether the language associated with a given functional automaton can be defined with a deterministic one, for sum, mean and discounted sum. The results on functionality and determinizability are expressed for the more general class of functional weighted automata over groups. This allows one to formulate within the same framework new results related to discounted sum automata and known results on sum and mean automata. Ratio automata do not fit within this general scheme and specific techniques are required to decide functionality. © 2012 Springer-Verlag.SCOPUS: cp.kinfo:eu-repo/semantics/publishe

TAGED Approximations for Temporal Properties Model-Checking

This paper investigates the use of tree automata with global equalities and disequalities (TAGED for short) in reachability analysis over term rewriting systems (TRSs). The reachability problem being in general undecidable on non terminating TRSs, we provide TAGED-based construction, and then design approximation-based semi-decision procedures to model-check useful temporal patterns on infinite state rewriting graphs. To show that the above TAGED-based construction can be effectively carried out, complexity analysis for rewriting TAGED-definable languages is given