On Deciding Local Theory Extensions via E-matching

Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures for theories of data types that commonly occur in software. This makes them important tools for automating verification problems. A limitation frequently encountered is that verification problems are often not fully expressible in the theories supported natively by the solvers. Many solvers allow the specification of application-specific theories as quantified axioms, but their handling is incomplete outside of narrow special cases. In this work, we show how SMT solvers can be used to obtain complete decision procedures for local theory extensions, an important class of theories that are decidable using finite instantiation of axioms. We present an algorithm that uses E-matching to generate instances incrementally during the search, significantly reducing the number of generated instances compared to eager instantiation strategies. We have used two SMT solvers to implement this algorithm and conducted an extensive experimental evaluation on benchmarks derived from verification conditions for heap-manipulating programs. We believe that our results are of interest to both the users of SMT solvers as well as their developers

Towards Realizability Checking of Contracts using Theories

Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate architectural descriptions and compositional reasoning rules, these techniques can be used to prove important safety properties about the architecture prior to system construction. Such proofs build from "leaf-level" assume/guarantee component contracts through architectural layers towards top-level safety properties. The proofs are built upon the premise that each leaf-level component contract is realizable; i.e., it is possible to construct a component such that for any input allowed by the contract assumptions, there is some output value that the component can produce that satisfies the contract guarantees. Without engineering support it is all too easy to write leaf-level components that can't be realized. Realizability checking for propositional contracts has been well-studied for many years, both for component synthesis and checking correctness of temporal logic requirements. However, checking realizability for contracts involving infinite theories is still an open problem. In this paper, we describe a new approach for checking realizability of contracts involving theories and demonstrate its usefulness on several examples.Comment: 15 pages, to appear in NASA Formal Methods (NFM) 201

Incremental bounded model checking for embedded software

Program analysis is on the brink of mainstream usage in embedded systems development. Formal verification of behavioural requirements, finding runtime errors and test case generation are some of the most common applications of automated verification tools based on bounded model checking (BMC). Existing industrial tools for embedded software use an off-the-shelf bounded model checker and apply it iteratively to verify the program with an increasing number of unwindings. This approach unnecessarily wastes time repeating work that has already been done and fails to exploit the power of incremental SAT solving. This article reports on the extension of the software model checker CBMC to support incremental BMC and its successful integration with the industrial embedded software verification tool BTC EMBEDDED TESTER. We present an extensive evaluation over large industrial embedded programs, mainly from the automotive industry. We show that incremental BMC cuts runtimes by one order of magnitude in comparison to the standard non-incremental approach, enabling the application of formal verification to large and complex embedded software. We furthermore report promising results on analysing programs with arbitrary loop structure using incremental BMC, demonstrating its applicability and potential to verify general software beyond the embedded domain