Linear Temporal Logic And Linear Dynamic Logic On Finite Traces

Abstract

In this paper we look into the assumption of interpreting LTL over finite traces. In particular we show that LTL_f, i.e., LTL under this assumption, is less expressive than what might appear at first sight, and that at essentially no computational cost one can make a significant increase in expressiveness while maintaining the same intuitiveness of LTL_f. Indeed, we propose a logic, LDL_f for Linear Dynamic Logic over finite traces, which borrows the syntax from Propositional Dynamic Logic PDL, but is interpreted over finite traces. Satisfiability, validity and logical implication (as well as model checking) for LDL_f are PSPACE-complete as for LTL_f (and LTL).