Fairness, assumptions, and guarantees for extended bounded response LTL+P synthesis

Abstract

AbstractRealizability and reactive synthesis from temporal logics are fundamental problems in formal verification. The complexity of these problems for linear temporal logic with past ( ) led to the identification of fragments with lower complexities and simpler algorithms. Recently, the logic of extended bounded response  ($$\textsf {LTL} _{\textsf {EBR} }\textsf {{+}P} $$ LTL EBR + P  for short) has been introduced. It allows one to express safety languages definable in  and it is provided with an efficient, fully symbolic algorithm for reactive synthesis. This paper features four related contributions. First, we introduce - , an extension of $$\textsf {LTL} _{\textsf {EBR} }\textsf {{+}P} $$ LTL EBR + P  with fairness conditions, assumptions, and guarantees that, on the one hand, allows one to express properties beyond the safety fragment and, on the other, it retains the efficiency of $$\textsf {LTL} _{\textsf {EBR} }\textsf {{+}P} $$ LTL EBR + P  in practice. Second, we the expressiveness of - starting from the expressiveness of its fragments. In particular, we prove that: (1) $$\textsf {LTL} _{\textsf {EBR} }\textsf {{+}P} $$ LTL EBR + P  is expressively complete with respect to the safety fragment of  , (2) the removal of past operators from $$\textsf {LTL} _{\textsf {EBR} }\textsf {{+}P} $$ LTL EBR + P  results into a loss of expressive power, and (3) - is expressively equivalent to the logic  of Bloem et al. Third, we provide a fully symbolic algorithm for the realizability problem from - specifications, that reduces it to a number of safety subproblems. Fourth, to ensure soundness and completeness of the algorithm, we propose and exploit a general framework for safety reductions in the context of realizability of (fragments of)  . The experimental evaluation shows promising results.