On abstraction refinement for program analyses in Datalog

A central task for a program analysis concerns how to efficiently find a program abstraction that keeps only information relevant for proving properties of interest. We present a new approach for finding such abstractions for program analyses written in Datalog. Our approach is based on counterexample-guided abstraction refinement: when a Datalog analysis run fails using an abstraction, it seeks to generalize the cause of the failure to other abstractions, and pick a new abstraction that avoids a similar failure. Our solution uses a boolean satisfiability formulation that is general, complete, and optimal: it is independent of the Datalog solver, it generalizes the failure of an abstraction to as many other abstractions as possible, and it identifies the cheapest refined abstraction to try next. We show the performance of our approach on a pointer analysis and a typestate analysis, on eight real-world Java benchmark programs

Domain-Type-Guided Refinement Selection Based on Sliced Path Prefixes

Abstraction is a successful technique in software verification, and interpolation on infeasible error paths is a successful approach to automatically detect the right level of abstraction in counterexample-guided abstraction refinement. Because the interpolants have a significant influence on the quality of the abstraction, and thus, the effectiveness of the verification, an algorithm for deriving the best possible interpolants is desirable. We present an analysis-independent technique that makes it possible to extract several alternative sequences of interpolants from one given infeasible error path, if there are several reasons for infeasibility in the error path. We take as input the given infeasible error path and apply a slicing technique to obtain a set of error paths that are more abstract than the original error path but still infeasible, each for a different reason. The (more abstract) constraints of the new paths can be passed to a standard interpolation engine, in order to obtain a set of interpolant sequences, one for each new path. The analysis can then choose from this set of interpolant sequences and select the most appropriate, instead of being bound to the single interpolant sequence that the interpolation engine would normally return. For example, we can select based on domain types of variables in the interpolants, prefer to avoid loop counters, or compare with templates for potential loop invariants, and thus control what kind of information occurs in the abstraction of the program. We implemented the new algorithm in the open-source verification framework CPAchecker and show that our proof-technique-independent approach yields a significant improvement of the effectiveness and efficiency of the verification process.Comment: 10 pages, 5 figures, 1 table, 4 algorithm

Abstraction in directed model checking

Abstraction is one of the most important issues to cope with large and infinite state spaces in model checking and to reduce the verification efforts. The abstract system is smaller than the original one and if the abstract system satisfies a correctness specification, so does the concrete one. However, abstractions may introduce a behavior violating the specification that is not present in the original system. This paper bypasses this problem by proposing the combination of abstraction with heuristic search to improve error detection. The abstract system is explored in order to create a database that stores the exact distances from abstract states to the set of abstract error states. To check, whether or not the abstract behavior is present in the original system, effcient exploration algorithms exploit the database as a guidance

Software Model Checking via Large-Block Encoding

The construction and analysis of an abstract reachability tree (ART) are the basis for a successful method for software verification. The ART represents unwindings of the control-flow graph of the program. Traditionally, a transition of the ART represents a single block of the program, and therefore, we call this approach single-block encoding (SBE). SBE may result in a huge number of program paths to be explored, which constitutes a fundamental source of inefficiency. We propose a generalization of the approach, in which transitions of the ART represent larger portions of the program; we call this approach large-block encoding (LBE). LBE may reduce the number of paths to be explored up to exponentially. Within this framework, we also investigate symbolic representations: for representing abstract states, in addition to conjunctions as used in SBE, we investigate the use of arbitrary Boolean formulas; for computing abstract-successor states, in addition to Cartesian predicate abstraction as used in SBE, we investigate the use of Boolean predicate abstraction. The new encoding leverages the efficiency of state-of-the-art SMT solvers, which can symbolically compute abstract large-block successors. Our experiments on benchmark C programs show that the large-block encoding outperforms the single-block encoding.Comment: 13 pages (11 without cover), 4 figures, 5 table