Narrow Results

We introduce a certain restriction of weighted automata over the rationals, called image-binary automata. We show that such automata accept the regular languages, can be exponentially more succinct than corresponding NFAs, and allow for polynomial complementation, union, and intersection. This compares favourably with unambiguous automata whose complementation requires a superpolynomial state blowup. We also study an infinite-word version, image-binary Büchi automata. We show that such automata are amenable to probabilistic model checking, similarly to unambiguous Büchi automata. We provide algorithms to translate $k$-ambiguous Büchi automata to image-binary Büchi automata, leading to model-checking algorithms with optimal computational complexity.

This paper addresses the challenges of symbolic model checking and language emptiness checking where the specification is given as an alternating Büchi automaton.

We introduce a novel version of Miyano and Hayashi's construction that allows us to directly convert an alternating automaton to a polynomially-sized symbolic structure. We thus avoid building an exponentially-sized explicit representation of the corresponding nondeterministic automaton.

For one-weak automata, Gastin and Oddoux' construction produces smaller automata than Miyano and Hayashi's construction. We present a (symbolic) hybrid approach that combines the benefits of both: while retaining full generality, it uses the cheaper construction for those parts of the automaton that are one-weak.

We performed a thorough experimental comparison of the explicit and symbolic approaches and several variants of Miyano and Hayashi's construction, using both BDD-based and SAT-based model checking techniques. The symbolic approaches clearly outperform the explicit one.

This paper considers the problem of computing the real convex hull of a finite set of n-dimensional integer vectors. The starting point is a finite-automaton representation of the initial set of vectors. The proposed method consists in computing a sequence of automata representing approximations of the convex hull and using extrapolation techniques to compute the limit of this sequence. The convex hull can then be directly computed from this limit in the form of an automaton-based representation of the corresponding set of real vectors. The technique is quite general and has been implemented.

We extend the concept of factorization on finite words to ω-rational languages and show how to compute them. We define a normal form for Büchi automata and introduce a universal automaton for Büchi automata in normal form. We prove that, for every ω-rational language, this Büchi automaton, based on factorization, is canonical and that it is the smallest automaton that contains the morphic image of every equivalent Büchi automaton in normal form.

In this paper we consider the extension of Nerode theorem to infinite trees. Unfortunately, we prove that this extension is not possible. We give some characterizations of recognizable and rational ω-tree sets in terms of ω-tree automata. We consider some complexity measures of recognizable and rational ω-tree sets and prove that these measures define infinite hierarchies.

We introduce various types of top-down pushdown infinite tree automata. We extend the Landweber-Staiger-Wagner hierarchy to pushdown infinite tree automata. We prove that the extension of Kleene’s theorem to pushdown infinite tree automata is not possible. We characterize recognizable (i.e. regular) infinite trees and extend Eilenberg’s theorem to ω-tree pushdown automata. We give some characterizations of infinite computations of nondeterministic context-free program schemes. We show that the equivalence problem for nondeterministic context-free program schemes is unsolvable.

Drawing on business rules for constructing business process models by a constraint-driven methodology is a distinct characteristic of declarative process modeling. Given the intricacies of business rules, there is a pragmatic need to conduct conflict-free assessments for business rules in an automatic manner. In this paper, business rules are stated in terms of restricted English by harnessing a group of predefined business rule templates. With linear temporal logic that serves as a semantic foundation for the business rule templates, a pair of business rules represented as a linear temporal logic specification is translated into an associated Büchi automaton via LTL2BA, LTL3BA and ltl2tgba. A Büchi automaton that accepts the empty language signifies that the two business rules are in conflict with each other. The suitability of the formal framework and the three automated tools is evaluated by an industry-level case study.

We investigate Büchi automata with weights for the transitions. Assuming that the weights are taken in a suitable ordered semiring, we show how to define the behaviors of these automata on infinite words. Our main result shows that the formal power series arising in this way are precisely the ones which can be constructed using ω-rational operations. This extends the classical Kleene–Schützenberger result for weighted finite automata to the case of infinite words and generalizes Büchi's theorem on languages of infinite words. We also derive versions of our main result for non-complete semirings and for other automata models.