Ultimate Automizer and the Search for Perfect Interpolants

Abstract

Abstract. Ultimate Automizer is a software verifier that generalizes proofs for traces to proofs for larger parts for the program. In recent years the portfolio of proof producers that are available to Ultimate has grown continuously. This is not only because more trace analysis algorithms have been implemented in Ultimate but also due to the continuous progress in the SMT community. In this paper we explain how Ultimate Automizer dynamically selects trace analysis algorithms and how the tool decides when proofs for traces are "good" enough for using them in the abstraction refinement. Verification ApproachUltimate Automizer (in the following called Automizer) is a software verifier that is able to check safety and liveness properties. The tool implements an automata-based [6] instance of the CEGAR scheme. In each iteration, we pick a trace (which is a sequence of statements) that leads from the initial location to the error location and check whether the trace is feasible (i.e., corresponds to an execution) or infeasible. If the trace is feasible, we report an error to the user; otherwise we compute a sequence of predicates along the trace as a proof of the trace's infeasibility. We call such a sequence of predicates a sequence of interpolants since each predicate "interpolates" between the set of reachable states and the set of states from which we cannot reach the error. In the refinement step of the CEGAR loop, we try to find all traces whose infeasibility can be shown with the given predicates and subtract these traces from the set of (potentially spurious) error traces that have not yet been analyzed. We use automata to represent sets of traces; hence the subtraction is implemented as an automata operation. The major difference to a classical CEGAR-based predicate abstraction is that we never have to do any logical reasoning (e.g., SMT solver calls) that involves predicates of different CEGAR iterations.We use this paper to explain how our tool obtains the interpolants that are used in the refinement step. The Ultimate program analysis framework

VeriAbs : Verification by Abstraction and Test Generation (Competition Contribution)

“…In this version, we additionally derive disjunctive invariants for correctness witnesses using abstract acceleration and abstract interpretation, and add them to the control flow automaton generated by CPAchecker. If all implemented techniques fail, we use techniques implemented in Ultimate Automizer v3204b741 [11] to generate correctness witnesses.…”

Efficient Strategies for CEGAR-Based Model Checking

“…4.2.4). Using a portfolio of refinements can combine the advantages of different methods [16,45]. Therefore, in this section we suggest strategies that calculate both forward and backward interpolants and pick the "better" one based on certain heuristics.…”

“…Ultimate Automizer [45] also works with a portfolio of refiners, including Craig interpolation, unsatisfiable cores, various SMT solvers and different ways to abstract a trace. They use a single measure for the quality of an interpolation, namely checking if the interpolant constitutes a Floyd-Hoare annotation.…”

“…However, there is usually no single best variant: different algorithms are suitable for different verification tasks [43]. Therefore, generic frameworks are also emerging, which provide configurability [14], combinations of different strategies for abstraction and refinement [2,45], and support for various kind of models [49,60]. Contributions In our paper, we make the following novel contributions.…”

Function Summarization Modulo Theories

“…Since McMillan's first application of interpolants in formal verification [26], interpolation has been applied in algorithms with various extensions in model checking [11,27,34,20,2,31,1,28,16,35,15,14,24]. Model checkers CPAchecker [8], SeaHorn [17], Ultimate Automizer [19] and others leverage interpolants in some form.…”