Freedom, Weakness, and Determinism: From Linear-Time to Branching-Time

Model checking is a method for the veri cation of systems with respect to their speci cations. Symbolic model-checking, which enables the veri cation of large systems, proceeds by calculating xed-point expressions over the system's set of states. The -calculus is a branching-time temporal logic with xed-point operators. As such, it is a convenient logic for symbolic modelchecking tools. In particular, the alternationfree fragment of -calculus has a restricted syntax, making the symbolic evaluation of its formulas computationally easy. Formally, it takes time that is linear in the size of the system. On the other hand, speci ers nd the -calculus inconvenient. In addition, speci ers often prefer to use linear-time formalisms. Such formalisms, however, cannot in general be translated to the alternation-free -calculus, and their symbolic evaluation involves nesting of xed-points, resulting in time complexity that is quadratic in the size of the system. In this paper we characterize linear-time properties that can be specied in the alternation-free -calculus. We show that a linear-time property can be speci ed in the alternation-free -calculus i it can be recognized Address: EECS Department, UC Berkeley, Berkeley CA 94720-1770, U.S.A. Email: [email protected], URL: http://www.eecs.berkeley.edu/ orna. Supported in part by ONR YIP award N00014-95-1-0520, by NSF CAREER award CCR-9501708, by NSF grant CCR9504469, by AFOSR contract F49620-93-1-0056, by ARO MURI grant DAAH-04-96-1-0341, by ARPA grant NAG2892, and by the SRC contract 95-DC-324.036. y Address: CS Department, Rice University, Houston TX 77005-1892, U.S.A. Email: [email protected], URL: http://www.cs.rice.edu/ vardi. Supported in part by NSF grants CCR-9628400 and CCR-9700061, and by a grant from the Intel Corporation. by a deterministic B uchi automaton. We study the problem of deciding whether a linear-time property, speci ed by either an automaton or an LTL formula, can be translated to an alternationfree -calculus formula, and describe the translation, when exists.