We present an algorithm to generate small Büchi automata for LTL formulae. We describe a heuristic approach consisting of three phases: rewriting of the formula, an optimized translation procedure, and simplification of the resulting automaton. We present a translation procedure that is optimal within a certain class of translation procedures. The simplification algorithm can be used for Buchi automata in general. It reduces the number of states and transitions, as well as the number and size of the accepting sets---possibly reducing the strength of the resulting automaton. This leads to more efficient model checking of lineartime logic formulae. We compare our method to previous work, and show that it is significantly more efficient for both random formulae, and formulae in common use and from the literature.

The standard technique for LTL model checking (M j) consists on translating the negation of the LTL specification, j, into a Büchi automaton A_φ, and then on checking if the product M × A_φ has an empty language. The efforts to maximize the efficiency of this process have so far concentrated on developing translation algorithms producing Büchi automata which are "as small as possible", under the implicit conjecture that this fact should make the final product smaller. In this paper we build on a different conjecture and present an alternative approach in which we generate instead Buchi automata which are "as deterministic as possible", in the sense that we try to reduce as much as we are able to the presence of non-deterministic decision states in A_&phi:. We motivate our choice and present some empirical tests to support this approach.

Abstract. Many different automata and algorithms have been investigated in the context of automata-theoretic LTL model checking. This article compares the behaviour of two variations on the widely used Büchi automaton, namely (i) a Büchi automaton where states are labelled with atomic propositions and transitions are unlabelled, and (ii) a form of testing automaton that can only observe changes in state propositions and makes use of special livelock acceptance states. We describe how these variations can be generated from standard Büchi automata, and outline an SCC-based algorithm for verification with testing automata. The variations are compared to standard automata in experiments with both random and human-generated Kripke structures and LTL X formulas, using SCC-based algorithms as well as a recent, improved version of the classic nested search algorithm. The results show that SCCbased algorithms outperform their nested search counterpart, but that the biggest improvements come from using the variant automata. Much work has been done on the generation of small automata, but small automata do not necessarily lead to small products when combined with the system being verified. We investigate the underlying factors for the superior performance of the new variations. 1

We present an algorithm for the conversion of very weak alternating Büchi automata into nondeterministic Büchi automata (NBA), and we introduce a local optimization criterion for deleting superfluous transitions in these NBA. We show how to use this algorithm in the translation of LTL formulas into NBA, matching the upper bounds of other LTL-to-NBA translations. We compare the NBA resulting from our translation to the results of two popular algorithms for the translation of LTL to generalized Büchi automata: the translation of Gerth et al. of 1995 (resulting in the GPVWautomaton), and the translation of Daniele et al. of 1999 (resulting in the DGV-automaton) which improves on the GPVW algorithm. We show that the redundancy check by syntactical implication used in the construction of the DGV-automaton is covered by our local optimization, that is, all transitions removed by the redundancy check will also be removed according to our local optimization criterion. Moreover, for a fixed input formula in next normal form, our locally optimized NBA from LTL and the locally optimized GPVW- and DGV-automaton are essentially the same. Both these results give a “structural ” explanation for the syntactic approaches by Gerth et al. and Daniele et al. We show that a bottom-up variant of our algorithm allows to pass simplifications of NBA for subformulas on to the NBA for the entire LTL formula. 1 1

Model checking addresses correctness of finite-state systems by formal methods. It automatically either proves the user-defined properties of the system correct, or...

Von den vielen Menschen, die mich bei der Erstellung dieser Dissertation unterstützt haben, möchte ich Thomas Wilke besonders hervorheben. Thomas stand mir stets mit Rat und Hilfe zur Seite und hat mich als Doktorand vorbildlich betreut. Als begeisterter, sorgfältiger Forscher und liebenswerter Mensch ist er mir ein wichtiges Vorbild. Gerne bedanke ich mich bei der Deutschen Forschungsgemeinschaft (DFG) für die finanzielle Unterstützung der Forschung, die zu dieser Arbeit geführt hat (Projektnummer 223228).

ur algorithm on the other hand outperforms Spin's algorithm as shown in Table 1. YAL2A Spin 1 < 0.01 s 9 ko 0.3 s 460 ko 2 < 0.01 s 11 ko 8 s 4,2 Mo 3 < 0.01 s 19 ko 4 mn 52 Mo 4 0.08 s 38 ko 5 h 30 970 Mo 5 0.6 s 48 ko 6 6.7 s 88 ko 7 54 s 176 ko 8 10 mn 248 ko 9 1 h 30 490 ko Table 1: Time and space comparison between YAL2A and SPIN on the formulas n , 1 n 9 The algorithms [GPVW95, DGV99, SB00, EH00] for building the Buchi automaton from the LTL formula consist of three phases. First, the formula is rewritten into some canonical form. Second a Buchi automaton is generated. Third, the automaton is simplied in order to get fewer states and fewer transitions.