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

Backward Reachability of Array-based Systems by SMT solving: Termination and Invariant Synthesis

The safety of infinite state systems can be checked by a backward reachability procedure. For certain classes of systems, it is possible to prove the termination of the procedure and hence conclude the decidability of the safety problem. Although backward reachability is property-directed, it can unnecessarily explore (large) portions of the state space of a system which are not required to verify the safety property under consideration. To avoid this, invariants can be used to dramatically prune the search space. Indeed, the problem is to guess such appropriate invariants. In this paper, we present a fully declarative and symbolic approach to the mechanization of backward reachability of infinite state systems manipulating arrays by Satisfiability Modulo Theories solving. Theories are used to specify the topology and the data manipulated by the system. We identify sufficient conditions on the theories to ensure the termination of backward reachability and we show the completeness of a method for invariant synthesis (obtained as the dual of backward reachability), again, under suitable hypotheses on the theories. We also present a pragmatic approach to interleave invariant synthesis and backward reachability so that a fix-point for the set of backward reachable states is more easily obtained. Finally, we discuss heuristics that allow us to derive an implementation of the techniques in the model checker MCMT, showing remarkable speed-ups on a significant set of safety problems extracted from a variety of sources.Comment: Accepted for publication in Logical Methods in Computer Scienc

Propositional Reasoning about Safety and Termination of Heap-Manipulating Programs

This paper shows that it is possible to reason about the safety and termination of programs handling potentially cyclic, singly-linked lists using propositional reasoning even when the safety invariants and termination arguments depend on constraints over the lengths of lists. For this purpose, we propose the theory SLH of singly-linked lists with length, which is able to capture non-trivial interactions between shape and arithmetic. When using the theory of bit-vector arithmetic as a background, SLH is efficiently decidable via a reduction to SAT. We show the utility of SLH for software verification by using it to express safety invariants and termination arguments for programs manipulating potentially cyclic, singly-linked lists with unrestricted, unspecified sharing. We also provide an implementation of the decision procedure and use it to check safety and termination proofs for several heap-manipulating programs

Program Analysis in A Combined Abstract Domain

Automated verification of heap-manipulating programs is a challenging task due to the complexity of aliasing and mutability of data structures used in these programs. The properties of a number of important data structures do not only relate to one domain, but to combined multiple domains, such as sorted list, priority queues, height-balanced trees and so on. The safety and sometimes efficiency of programs do rely on the properties of those data structures. This thesis focuses on developing a verification system for both functional correctness and memory safety of such programs which involve heap-based data structures. Two automated inference mechanisms are presented for heap-manipulating programs in this thesis. Firstly, an abstract interpretation based approach is proposed to synthesise program invariants in a combined pure and shape domain. Newly designed abstraction, join and widening operators have been defined for the combined domain. Furthermore, a compositional analysis approach is described to discover both pre-/post-conditions of programs with a bi-abduction technique in the combined domain. As results of my thesis, both inference approaches have been implemented and the obtained results validate the feasibility and precision of proposed approaches. The outcomes of the thesis confirm that it is possible and practical to analyse heap-manipulating programs automatically and precisely by using abstract interpretation in a sophisticated combined domain

Biabduction (and related problems) in array separation logic

We investigate array separation logic (\mathsf {ASL}), a variant of symbolic-heap separation logic in which the data structures are either pointers or arrays, i.e., contiguous blocks of memory. This logic provides a language for compositional memory safety proofs of array programs. We focus on the biabduction problem for this logic, which has been established as the key to automatic specification inference at the industrial scale. We present an \mathsf {NP} decision procedure for biabduction in \mathsf {ASL}, and we also show that the problem of finding a consistent solution is \mathsf {NP}-hard. Along the way, we study satisfiability and entailment in \mathsf {ASL}, giving decision procedures and complexity bounds for both problems. We show satisfiability to be \mathsf {NP}-complete, and entailment to be decidable with high complexity. The surprising fact that biabduction is simpler than entailment is due to the fact that, as we show, the element of choice over biabduction solutions enables us to dramatically reduce the search space

A survey of new trends in symbolic execution for software testing and analysis

Abstract Symbolic execution is a well-known program analysis technique which represents program inputs with symbolic values instead of concrete, initialized, data and executes the program by manipulating program expressions involving the symbolic values. Symbolic execution has been proposed over three decades ago but recently it has found renewed interest in the research community, due in part to the progress in decision procedures, availability of powerful computers and new algorithmic developments. We provide here a survey of some of the new research trends in symbolic execution, with particular emphasis on applications to test generation and program analysis. We first describe an approach that handles complex programming constructs such as input recursive data structures, arrays, as well as multithreading. Furthermore, we describe recent hybrid techniques that combine concrete and symbolic execution to overcome some of the inherent limitations of symbolic execution, such as handling native code or availability of decision procedures for the application domain. We follow with a discussion of techniques that can be used to limit the (possibly infinite) number of symbolic configurations that need to be analyzed for the symbolic execution of looping programs. Finally, we give a short survey of interesting new applications, such as predictive testing, invariant inference

Biabduction (and related problems) in array separation logic

We investigate array separation logic (\mathsf {ASL}), a variant of symbolic-heap separation logic in which the data structures are either pointers or arrays, i.e., contiguous blocks of memory. This logic provides a language for compositional memory safety proofs of array programs. We focus on the biabduction problem for this logic, which has been established as the key to automatic specification inference at the industrial scale. We present an \mathsf {NP} decision procedure for biabduction in \mathsf {ASL}, and we also show that the problem of finding a consistent solution is \mathsf {NP}-hard. Along the way, we study satisfiability and entailment in \mathsf {ASL}, giving decision procedures and complexity bounds for both problems. We show satisfiability to be \mathsf {NP}-complete, and entailment to be decidable with high complexity. The surprising fact that biabduction is simpler than entailment is due to the fact that, as we show, the element of choice over biabduction solutions enables us to dramatically reduce the search space