Relational Symbolic Execution

Symbolic execution is a classical program analysis technique used to show that programs satisfy or violate given specifications. In this work we generalize symbolic execution to support program analysis for relational specifications in the form of relational properties - these are properties about two runs of two programs on related inputs, or about two executions of a single program on related inputs. Relational properties are useful to formalize notions in security and privacy, and to reason about program optimizations. We design a relational symbolic execution engine, named RelSym which supports interactive refutation, as well as proving of relational properties for programs written in a language with arrays and for-like loops

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

Finite Countermodel Based Verification for Program Transformation (A Case Study)

Both automatic program verification and program transformation are based on program analysis. In the past decade a number of approaches using various automatic general-purpose program transformation techniques (partial deduction, specialization, supercompilation) for verification of unreachability properties of computing systems were introduced and demonstrated. On the other hand, the semantics based unfold-fold program transformation methods pose themselves diverse kinds of reachability tasks and try to solve them, aiming at improving the semantics tree of the program being transformed. That means some general-purpose verification methods may be used for strengthening program transformation techniques. This paper considers the question how finite countermodels for safety verification method might be used in Turchin's supercompilation method. We extract a number of supercompilation sub-algorithms trying to solve reachability problems and demonstrate use of an external countermodel finder for solving some of the problems.Comment: In Proceedings VPT 2015, arXiv:1512.0221

Generating Property-Directed Potential Invariants By Backward Analysis

This paper addresses the issue of lemma generation in a k-induction-based formal analysis of transition systems, in the linear real/integer arithmetic fragment. A backward analysis, powered by quantifier elimination, is used to output preimages of the negation of the proof objective, viewed as unauthorized states, or gray states. Two heuristics are proposed to take advantage of this source of information. First, a thorough exploration of the possible partitionings of the gray state space discovers new relations between state variables, representing potential invariants. Second, an inexact exploration regroups and over-approximates disjoint areas of the gray state space, also to discover new relations between state variables. k-induction is used to isolate the invariants and check if they strengthen the proof objective. These heuristics can be used on the first preimage of the backward exploration, and each time a new one is output, refining the information on the gray states. In our context of critical avionics embedded systems, we show that our approach is able to outperform other academic or commercial tools on examples of interest in our application field. The method is introduced and motivated through two main examples, one of which was provided by Rockwell Collins, in a collaborative formal verification framework.Comment: In Proceedings FTSCS 2012, arXiv:1212.657

Verification and refutation of C programs based on k -induction and invariant inference

From Springer Nature via Jisc Publications RouterHistory: registration 2020-04-23, online 2020-05-18, pub-electronic 2020-05-18, pub-print 2021-04Publication status: PublishedFunder: University of ManchesterAbstract: DepthK is a source-to-source transformation tool that employs bounded model checking (BMC) to verify and falsify safety properties in single- and multi-threaded C programs, without manual annotation of loop invariants. Here, we describe and evaluate a proof-by-induction algorithm that combines k-induction with invariant inference to prove and refute safety properties. We apply two invariant generators to produce program invariants and feed these into a k-induction-based verification algorithm implemented in DepthK, which uses the efficient SMT-based context-bounded model checker (ESBMC) as sequential verification back-end. A set of C benchmarks from the International Competition on Software Verification (SV-COMP) and embedded-system applications extracted from the available literature are used to evaluate the effectiveness of the proposed approach. Experimental results show that k-induction with invariants can handle a wide variety of safety properties, in typical programs with loops and embedded software applications from the telecommunications, control systems, and medical domains. The results of our comparative evaluation extend the knowledge about approaches that rely on both BMC and k-induction for software verification, in the following ways. (1) The proposed method outperforms the existing implementations that use k-induction with an interval-invariant generator (e.g., 2LS and ESBMC), in the category ConcurrencySafety, and overcame, in others categories, such as SoftwareSystems, other software verifiers that use plain BMC (e.g., CBMC). Also, (2) it is more precise than other verifiers based on the property-directed reachability (PDR) algorithm (i.e., SeaHorn, Vvt and CPAchecker-CTIGAR). This way, our methodology demonstrated improvement over existing BMC and k-induction-based approaches

PrIC3: Property Directed Reachability for MDPs

IC3 has been a leap forward in symbolic model checking. This paper proposes PrIC3 (pronounced pricy-three), a conservative extension of IC3 to symbolic model checking of MDPs. Our main focus is to develop the theory underlying PrIC3. Alongside, we present a first implementation of PrIC3 including the key ingredients from IC3 such as generalization, repushing, and propagation