We study the expressive power of linear propositional temporal logic interpreted on finite sequences or words. We first give a transparent proof of the fact that a formal language is expressible in this logic if and only if its syntactic semigroup is finite and aperiodic. This gives an effective algorithm to decide whether a given rational language is expressible. Our main result states a similar condition for the "restricted" temporal logic (RTL), obtained by discarding the "until" operator. A formal language is RTL-expressible if and only if its syntactic semigroup is finite and satisfies a certain simple algebraic condition. This leads to a polynomial time algorithm to check whether the formal language accepted by an n-state deterministic automaton is RTL-expressible. * Research on this paper was partially supported by PRC "Mathématiques et Informatique".
Simultaneous investigation of NF2, SMARCB1, LZTR1, and SMARCE1 is a key element in the differential diagnosis of NF2, schwannomatosis, and meningiomatosis. The targeted NGS strategy is suitable for the identification of NF2 mosaicism in blood and for the investigation of tumors from these patients.
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