TY - JOUR
T1 - From linear time to branching time
AU - Kupferman, Orna
AU - Vardi, Moshe Y.
PY - 2005/4
Y1 - 2005/4
N2 - Model checking is a method for the verification of systems with respect to their specifications. Symbolic model-checking, which enables the verification of large systems, proceeds by calculating fixed-point expressions over the system's set of states. The μ-calculus is a branching-time temporal logic with fixed-point operators. As such, it is a convenient logic for symbolic model-checking tools. In particular, the alternation-free fragment of μ-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, specifiers find the μ-calculus inconvenient. In addition, specifiers often prefer to use linear-time formalisms. Such formalisms, however, cannot in general be translated to the alternation-free μ-calculus, and their symbolic evaluation involves nesting of fixed-points, resulting in time complexity that is quadratic in the size of the system. In this article, we characterize linear-time properties that can be specified in the alternation-free μ-calculus. We show that a linear-time property can be specified in the alternation-free μ-calculus iff it can be recognized by a deterministic Büchi automaton. We study the problem of deciding whether a linear-time property, specified by either an automaton or an LTL formula, can be translated to an alternation-free μ.-calculus formula, and describe the translation, when possible.
AB - Model checking is a method for the verification of systems with respect to their specifications. Symbolic model-checking, which enables the verification of large systems, proceeds by calculating fixed-point expressions over the system's set of states. The μ-calculus is a branching-time temporal logic with fixed-point operators. As such, it is a convenient logic for symbolic model-checking tools. In particular, the alternation-free fragment of μ-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, specifiers find the μ-calculus inconvenient. In addition, specifiers often prefer to use linear-time formalisms. Such formalisms, however, cannot in general be translated to the alternation-free μ-calculus, and their symbolic evaluation involves nesting of fixed-points, resulting in time complexity that is quadratic in the size of the system. In this article, we characterize linear-time properties that can be specified in the alternation-free μ-calculus. We show that a linear-time property can be specified in the alternation-free μ-calculus iff it can be recognized by a deterministic Büchi automaton. We study the problem of deciding whether a linear-time property, specified by either an automaton or an LTL formula, can be translated to an alternation-free μ.-calculus formula, and describe the translation, when possible.
KW - Alternation-free μ-calculus
KW - Linear temporal logic
UR - http://www.scopus.com/inward/record.url?scp=16644363102&partnerID=8YFLogxK
U2 - 10.1145/1055686.1055689
DO - 10.1145/1055686.1055689
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AN - SCOPUS:16644363102
SN - 1529-3785
VL - 6
SP - 273
EP - 294
JO - ACM Transactions on Computational Logic
JF - ACM Transactions on Computational Logic
IS - 2
ER -