Aborts vs Resets in Linear Temporal Logic

There has been a major emphasis recently in the semiconductor industry on designing industrial-strength property specification languages (PSLs). Two major languages are ForSpec and Sugar 2.0, which are both extensions of Pnueli’s LTL. Both ForSpec and Sugar 2.0 directly support reset/abort signals, in which a check for a property ψ may be terminated and declared successful by an reset/abort signal, provided the check has not yet failed. ForSpec and Sugar 2.0, however, differ in their definition of failure. The definition of failure in ForSpec is syntactic, while the definition in Sugar 2.0 is semantic. In this work we examine the implications of this distinction between the two approaches, which we refer to as the reset approach (for ForSpec) and the abort approach (for Sugar 2.0). In order to focus on the reset/abort issue, we do not consider the full languages, which are quite rich, but rather the extensions of LTL with the reset/abort constructs. We show that the distinction between syntactic and semantic failure has a dramatic impact on the complexity of using the language in a model-checking tool. We prove that Reset-LTL enjoys the “fast-compilation property”: there is a linear translation of Reset-LTL formulas into alternating Büchi automata, which implies a linear translation of Reset-LTL formulas into a symbolic representation of nondeterministic Büchi automata. In contrast, the translation of Abort-LTL formulas into alternating Büchi automata is nonelementary (i.e., cannot be bounded by a stack of exponentials of a bounded height); each abort yields an exponential blow-up in the translation. This complexity bounds also apply to model checking; model checking Reset-LTL formulas is exponential in the size of the property, while model checking Abort-LTL formulas is nonelementary in the size of the property (the same bounds apply to satisfiability checking).