Real-time MTL with durations as SMT with applications to schedulability analysis

Abstract

This paper introduces a synthesis procedure for the satisfiability problem of RMTL-D formulas as SAT solving modulo theories. RMTL-D is a real-time version of metric temporal logic (MTL) extended by a duration quantifier allowing to measure time durations. For any given formula, a SAT instance modulo the theory of arrays, uninterpreted functions with equality and non-linear real-arithmetic is synthesized and may then be further investigated using appropriate SMT solvers. We show the benefits of using RMTL-D with the given SMT encoding on a diversified set of examples that include in particular its application in the area of schedulability analysis. Therefore, we introduce a simple language for formalizing schedulability problems and show how to formulate timing constraints as RMTL-D formulas. Our practical evaluation based on our synthesis and Z3 as back-end SMT solver also shows the feasibility of the overall approach.