A Translation of Weighted LTL Formulas to Weighted Buchi Automata over omega-valuation Monoids

In this paper we introduce a weighted LTL over product omega-valuation monoids that satisfy specific properties. We also introduce weighted generalized Buchi automata with epsilon-transitions, as well as weighted Buchi automata with epsilon-transitions over product omega-valuation monoids and prove that these two models are expressively equivalent and also equivalent to weighted Buchi automata already introduced in the literature. We prove that every formula of a syntactic fragment of our logic can be effectively translated to a weighted generalized Buchi automaton with epsilon-transitions. For generalized product omega-valuation monoids that satisfy specific properties we define a weighted LTL, weighted generalized Buchi automata with epsilon-transitions, and weighted Buchi automata with epsilon-transitions, and we prove the aforementioned results for generalized product omega-valuation monoids as well. The translation of weighted LTL formulas to weighted generalized Buchi automata with epsilon-transitions is now obtained for a restricted syntactical fragment of the logic.

Two Effective Properties of ω-Rational Functions

We prove two new effective properties of rational functions over infinite words which are realized by finite state Büchi transducers. Firstly, for each such function [Formula: see text], one can construct a deterministic Büchi automaton [Formula: see text] accepting a dense [Formula: see text]-subset of [Formula: see text] such that the restriction of [Formula: see text] to [Formula: see text] is continuous. Secondly, we give a new proof of the decidability of the first Baire class for synchronous [Formula: see text]-rational functions from which we get an extension of this result involving the notion of Wadge classes of regular [Formula: see text]-languages.

A Framework-Driven Comparison of Automata-Based Tools for Identifying Business Rule Conflicts

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.

The complexity of weakly recognizing morphisms

Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of ω-regular languages, i.e., a set of infinite words is weakly recognizable by such a morphism if and only if it is accepted by some Büchi automaton. We study the descriptional complexity of various constructions and the computational complexity of various decision problems for weakly recognizing morphisms. The constructions we consider are the conversion from and to Büchi automata, the conversion into strongly recognizing morphisms, as well as complementation. We also show that the fixed membership problem is NC1-complete, the general membership problem is in L and that the inclusion, equivalence and universality problems are NL-complete. The emptiness problem is shown to be NL-complete if the input is given as a non-surjective morphism.

On the Strength of Unambiguous Tree Automata

This work is a study of the class of non-deterministic automata on infinite trees that are unambiguous i.e. have at most one accepting run on every tree. The motivating question asks if the fact that an automaton is unambiguous implies some drop in the descriptive complexity of the language recognised by the automaton. As it turns out, such a drop occurs for the parity index and does not occur for the weak parity index.More precisely, given an unambiguous parity automaton [Formula: see text] of index [Formula: see text], we show how to construct an alternating automaton [Formula: see text] which accepts the same language, but is simpler in terms of the acceptance condition. In particular, if [Formula: see text] is a Büchi automaton ([Formula: see text]) then [Formula: see text] is a weak alternating automaton. In general, [Formula: see text] belongs to the class [Formula: see text], what implies that it is simultaneously of alternating index [Formula: see text] and of the dual index [Formula: see text]. The transformation algorithm is based on a separation procedure of Arnold and Santocanale (2005).In the case of non-deterministic automata with the weak parity condition, we provide a separation procedure analogous to the one used above. However, as illustrated by examples, this separation procedure cannot be used to prove a complexity drop in the weak case, as there is no such drop.

Statistical Automaton for Verifying Temporal Properties and Computing Information on Traces

Verification is decisive for embedded software. The goal of this work is to verify temporal properties on industrial applications, with the help of formal dynamic analysis. The approach presented in this paper is composed of three steps: formalization of temporal properties using an adequate language, generation of execution traces from a given property and verification of this property on execution traces. This paper focuses on the verification step. Use of a new kind of Büchi automaton has been proposed to provide an efficient verification taking into account the industrial needs and constraints. A prototype has been developed and used to carry out experiments on different anonymous real industrial applications.

FACTORIZATIONS AND UNIVERSAL AUTOMATON OF OMEGA LANGUAGES

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.