Abstract
Interpreting temporal logics on finite traces has specific use in many fields, and it attracts more and more attention in recent years. Foundation formulas (FL for short) is the core part of PSL, which has once been an industrial standard of specification language accepted by IEEE, and has now been adopted in SystemVerilog. We in this paper present a variant of FL, called FL\(^{res}\), whose semantics is defined w.r.t. finite words. In comparison to the original FL, the only syntactic restriction is that the “length-matching and” operator cannot appear in the first argument when doing concatenation. This restriction in syntax would not change the expressiveness, whereas could gain a much succinct automata based decision procedure. Namely, an FL\(^{res}\) formula \(\varphi \) can be equivalently transformed into a 2-way (or, stuttering) alternating finite automaton with \(\mathcal {O}(|\varphi |)\) states. Subsequently, one can convert it to a 1-way nondeterministic finite automaton with \(2^{\mathcal {O}(|\varphi |)}\) states.
Supported by NSFC under grant Nos 61872371, 61802415, and U19A2062.
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Notes
- 1.
Because, SERE and RE are the same in expressiveness. Our logic uses a restricted version of SERE, whereas it subsumes standard RE.
- 2.
For example, the language of \( \left( a^+ \& \& (a^+;b)\right) ;b^+\) is empty, whereas \( (a^+;b^+) \& \& (a^+;b;b^+)\) matches abb.
- 3.
We assume \(Q_1\cap Q_2=\emptyset \) in the sequel. Otherwise, just need a systematic state renaming.
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Liu, W., Yin, L., Li, T. (2020). Compiling FL\(^{res}\) on Finite Words. In: Pang, J., Zhang, L. (eds) Dependable Software Engineering. Theories, Tools, and Applications. SETTA 2020. Lecture Notes in Computer Science(), vol 12153. Springer, Cham. https://doi.org/10.1007/978-3-030-62822-2_7
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