Generalized Buchi Automata Research Articles

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.

A Better Translation From LTL to Transition-Based Generalized Büchi Automata

Translating linear temporal logic (LTL) formulas into Buchi automata is one of the most important aspects of LTL model checking. Certain successful algorithms, such as LTL2BA and SPOT, first translate an LTL formula into a transition-based generalized Buchi automaton (TGBA) and then degeneralize it into a Buchi automaton. This paper focuses on achieving a better translation from LTL to TGBA and analyzing the performance of every step of the algorithm. We decompose the translation into three steps to give a step-wise description and improve all three steps. The first step is the basic translation without acceptance conditions and simplifications, which combines the advantages of both LTL2BA and SPOT. Second, we introduce a new definition of acceptance conditions. Our proofs and experiments have shown that our technique is more efficient and improves the degeneralization ability. Finally, we introduce the simplifications of our algorithm. We focus on not only producing better final Buchi automata but also minimizing intermediate automata, which can reduce the execution time.

Efficient approach of translating LTL formulae into Büchi automata

In explicit-state model checking, system properties are typically expressed in linear temporal logic (LTL), and translated into a Buchi automaton (BA) to be checked. In order to improve performance of the conversion algorithm, some model checkers involve the intermediate automata, such as a generalized Buchi automaton (GBA). The de-generalization is a translation from a GBA to a BA. In this paper, we present a conversion algorithm to translate an LTL formula to a BA directly. A labeling, acceptance degree, is presented to record acceptance conditions satisfied in each state and transition. Acceptance degree is a set of U-subformulae or F-subformulae of the given LTL formula. According to the acceptance degree, on-the-fly degeneralization algorithm, which is different from the standard de-generalization algorithm, is conceived and implemented. On-the-fly de-generalization algorithm is carried out during the expansion of the given LTL formula. It is performed in the case of the given LTL formula contains U-subformulae and F-subformulae, that is, the on-the-fly de-generalization algorithm is performed as required. In order to get a more deterministic BA, the shannon expansion is used recursively during expanding LTL formulae. Ordered binary decision diagrams are used to represent the BA and simplify LTL formulae.We compare the conversion algorithm presented in this paper to previousworks, and show that it is more efficient for five families LTL formulae in common use and four sets of random formulae generated by LBTT (an LTL-to-Buchi translator testbench).

Truly Bitstate-Hashing for SCC-Based Emptiness Checking Algorithms

The paper proposes an improvement for SCC-based emptiness checking algorithms,which combines the advantages of SCC-based and nested depth first search for finding a cycle meeting all sets of acceptance conditions.The new algorithm uses the method of bitstate-hashing during emptiness checking for transition-based generalized Buchi automata,and the performance outperforms that of Couvreur′s.Meanwhile,the performance for finding a counterexample is the same as that of SCC-based ones.

Bridging the gap between fair simulation and trace inclusion

The paper considers the problem of checking abstraction between two finite-state fair discrete systems . In automata-theoretic terms this is trace inclusion between two nondeterministic Streett automata. We propose to reduce this problem to an algorithm for checking fair simulation between two generalized Büchi automata. For solving this question we present a new triply nested μ -calculus formula which can be implemented by symbolic methods. We then show that every trace inclusion of this type can be solved by fair simulation, provided we augment the concrete system (the contained automaton) by an appropriate ‘non-constraining’ automaton. This establishes that fair simulation offers a complete method for checking trace inclusion for finite-state systems. We illustrate the feasibility of the approach by algorithmically checking abstraction between finite state systems whose abstraction could only be verified by deductive methods up to now.