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On the Relationship between LTL Normal Forms and Buechi Automata

2012/07/17 by Jianwen Li, Li, Jianwen, Geguang Pu +9
Computer Science · #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Formal Methods in Verification #Logic, programming, and type systems #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1207.3866

openalex publication_date 2012/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the problem of translating LTL formulas to Buechi automata. We first translate the given LTL formula into a special disjuctive-normal form (DNF). The formula will be part of the state, and its DNF normal form specifies the atomic properties that should hold immediately (labels of the transitions) and the formula that should hold afterwards (the corresponding successor state). Surprisingly, if the given formula is Until-free or Release-free, the Buechi automaton can be obtained directly in this manner. For a general formula, the construction is slightly involved: an additional component will be needed for each formula that helps us to identify the set of accepting states. Notably, our construction is an on-the-fly construction, and the resulting Buechi automaton has in worst case 22n+1 states where n denotes the number of subformulas. Moreover, it has a better bound 2n+1 when the formula is Until- (or Release-) free.

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