| R. Szelepcsinyi. The method of forced enumeration for nondeterministic automata. Acta Informatica, 26:279--284, 1988. |
....we can specify the expression in the right with a fixed nonfair transition system, we are done. Proof of Theorem 2 # 2 The proof in [Jon75] is for the reachability problem. Yet, for every problem P , we have that P is NLOGSPACE complete if and only if P is co NLOGSPACE complete (see [Imm88, Sze88] for NLOGSPACE = co NLOGSPACE; the argument for the completeness is easy) 12 Chicago Journal of Theoretical Computer Science 1998 2 Kupferman and Vardi Verification of Systems 3.2 3.2 The Simulation Problem Theorem 3 The simulation problem is PTIME complete. Proof of Theorem 3 The upper ....
R. Szelepcsinyi. The method of forced enumeration for nondeterministic automata. Acta Informatica, 26:279--284, 1988.
....indifferent. Theorem 3.5 Given a module M , the problem of checking M for indifference is NLOGSPACE complete. Proof. For the upper bound, we show that checking whether M is not indifferent can be done in NLOGSPACE. The result then follows from the NLOGSPACE = co NLOGSPACE equivalence [Imm88, Sze88] Let M = hAP; W;W 0 ; R; L; ffi. By Theorem 3.4, M is not indifferent iff there exists an initial state w i 0 2 W 0 such that the language L(M i ) is not a singleton. The algorithm searches for a witness for M not being indifferent. For that, it guesses an initial state w i 0 and two ....
R. Szelepcsinyi. The method of forced enumeration for nondeterministic automata. Acta Informatica, 26:279--284, 1988.
....transition system, we are done. 3.2 The Complexity of the Simulation Problem Theorem 3.3 The simulation problem is PTIME complete. 1 The proof in [Jon75] is for the reachability problem. Yet, for every problem P , we have that P is NLOGSPACE complete iff P is co NLOGSPACE complete (see [Imm88, Sze88] for NLOGSPACE=coNLOGSPACE. The argument for the completeness is easy) Proof: The upper bound is given in [Mil80] The lower bound follows from the reduction in [BGS92] the reduction there proves PTIME hardness for bisimulation, but it is valid also for simulation) Theorem 3.4 The ....
R. Szelepcsinyi. The method of forced enumeration for nondeterministic automata. Acta Informatica, 26:279--284, 1988.
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