How to compute worst-case execution time by optimization modulo theory and a clever encoding of program semantics

Abstract

In systems with hard real-time constraints, it is necessary to compute upper bounds on the worst-case execution time (WCET) of programs; the closer the bound to the real WCET, the better. This is especially the case of synchronous reactive control loops with a fixed clock; the WCET of the loop body must not exceed the clock period.We compute the WCET (or at least a close upper bound thereof) as the solution of an optimization modulo theory problem that takes into account the semantics of the program, in contrast to other methods that compute the longest path whether or not it is feasible according to these semantics. Optimization modulo theory extends satisfiability modulo theory (SMT) to maximization problems.Immediate encodings of WCET problems into SMT yield formulas intractable for all current production-grade solvers -this is inherent to the DPLL(T) approach to SMT implemented in these solvers. By conjoining some appropriate "cuts" to these formulas, we considerably reduce the computation time of the SMT-solver.We experimented our approach on a variety of control programs, using the OTAWA analyzer both as baseline and as underlying microarchitectural analysis for our analysis, and show notable improvement on the WCET bound on a variety of benchmarks and control programs.

WCET analysis in shared resources real-time systems with TDMA buses

“…Henry et al [9] demonstrate how to measure the worst-case execution time using Bounded Model Checking. An SMT expressions is generated to encode the analyzed program and its execution time.…”

“…An SMT-solver is a program used to resolve the SMT expressions to answer the aforementioned question. In [9], the authors use a binary search method to find an upper bound of the execution time and disprove the existence of a solution with an execution time greater than the WCET. The semantics of the program can be used in determining feasible paths.…”

“…We extend the work of [9] to include the model of the shared bus accesses. This model is given in Section 3.1.…”

“…The encoding of blocks that do not access the shared bus comes straightforward from the previous work by Henry et al [9]. A variable c i j is associated to each transition between blocks i and j.…”

“…Henry et al [9] proposed an SMT-based approach to encode the analyzed program into SMT expressions in order to estimate the WCET. An SMT-solver is used to find the longest feasible path exhibiting the worst-case execution time.…”