TY - GEN
T1 - On ω-automata and temporal logic
AU - Safra, Shmuel
AU - Vardi, Moshe Y.
PY - 1989
Y1 - 1989
N2 - We study here the use of different representation for infinitary regular languages in extended temporal logic. We focus on three different kinds of acceptance conditions for finite automata on infinite words, due to J.R. Buechi, R.S. Streett, and E.A. Emerson and C.L. Lei (EL), and we study their computational properties. Our finding is that Buechi, Streett, and EL automata span a spectrum of succintness. EL automata are exponentially more succinct than Buechi automata, and complementation of EL automata is doubly exponential. Streett automata are of intermediate complexity. While translating from Streett automata to Buechi automata involves an exponential blow-up, so does that translation from EL automata to Streett automata. Furthermore, even though Streett automata are exponentially more succint than Buechi automata, complementation of Streett automata is only exponential. As a result, we show that the decision problem for ETLEL, where temporal connectives are represented by EL automata, is EXPSPACE-complete, and the decision problem for ETLS, where temporal connectives are represented by Streett automata, is PSPACE-complete.
AB - We study here the use of different representation for infinitary regular languages in extended temporal logic. We focus on three different kinds of acceptance conditions for finite automata on infinite words, due to J.R. Buechi, R.S. Streett, and E.A. Emerson and C.L. Lei (EL), and we study their computational properties. Our finding is that Buechi, Streett, and EL automata span a spectrum of succintness. EL automata are exponentially more succinct than Buechi automata, and complementation of EL automata is doubly exponential. Streett automata are of intermediate complexity. While translating from Streett automata to Buechi automata involves an exponential blow-up, so does that translation from EL automata to Streett automata. Furthermore, even though Streett automata are exponentially more succint than Buechi automata, complementation of Streett automata is only exponential. As a result, we show that the decision problem for ETLEL, where temporal connectives are represented by EL automata, is EXPSPACE-complete, and the decision problem for ETLS, where temporal connectives are represented by Streett automata, is PSPACE-complete.
UR - http://www.scopus.com/inward/record.url?scp=0024864868&partnerID=8YFLogxK
U2 - 10.1145/73007.73019
DO - 10.1145/73007.73019
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AN - SCOPUS:0024864868
SN - 0897913078
SN - 9780897913072
T3 - Proc Twenty First Annu ACM Symp Theory Comput
SP - 127
EP - 137
BT - Proc Twenty First Annu ACM Symp Theory Comput
PB - Association for Computing Machinery (ACM)
T2 - Proceedings of the Twenty First Annual ACM Symposium on Theory of Computing
Y2 - 15 May 1989 through 17 May 1989
ER -