Extended temporal logic revisited

A key issue in the design of a model-checking tool is the choice of the formal language with which properties are specified. It is now recognized that a good language should extend linear temporal logic with the ability to specify all ω-regular properties. Also, designers, who are familiar with finite-state machines, prefer extensions based on automata than these based on fixed points or propositional quantification. Early extensions of linear temporal logic with automata use nondeterministic Büchi automata. Their drawback has been inability to refer to the past and the asymmetrical structure of nondeterministic automata. In this work we study an extension of linear temporal logic, called ETL_2a, that uses two-way alternating automata as temporal connectives. Two way automata can traverse the input word back and forth and they are exponentially more succinct than one-way automata. Alternating automata combine existential and universal branching and they are exponentially more succinct than nondeterministic automata. The rich structure of two-way alternating automata makes ETL_2a a very powerful and convenient logic. We show that ETL2a formulas can be translated to nondeterministic Büchi automata with an exponential blow up. It follows that the satisfiability and model-checking problems for ETL_2a are PSPACE-complete, as are the ones for LTL and its earlier extensions with automata. So, in spite of the succinctness of two-way and alternating automata, the advantages of ETL_2a are obtained without a major increase in space complexity. The recent acceptance of alternating automata by the industry and the development of symbolic procedures for handling them make us optimistic about the practicality of ETL_2a.