on collecting semantics for program analysis

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Combining Forward and Backward Abstract Interpretation of Horn Clauses

Alternation of forward and backward analyses is a standard technique in abstract interpretation of programs, which is in particular useful when we wish to prove unreachability of some undesired program states. The current state-of-the-art technique for combining forward (bottom-up, in logic programming terms) and backward (top-down) abstract interpretation of Horn clauses is query-answer transformation. It transforms a system of Horn clauses, such that standard forward analysis can propagate constraints both forward, and backward from a goal. Query-answer transformation is effective, but has issues that we wish to address. For that, we introduce a new backward collecting semantics, which is suitable for alternating forward and backward abstract interpretation of Horn clauses. We show how the alternation can be used to prove unreachability of the goal and how every subsequent run of an analysis yields a refined model of the system. Experimentally, we observe that combining forward and backward analyses is important for analysing systems that encode questions about reachability in C programs. In particular, the combination that follows our new semantics improves the precision of our own abstract interpreter, including when compared to a forward analysis of a query-answer-transformed system.Comment: Francesco Ranzato. 24th International Static Analysis Symposium (SAS), Aug 2017, New York City, United States. Springer, Static Analysi

Static Safety for an Actor Dedicated Process Calculus by Abstract Interpretation

The actor model eases the definition of concurrent programs with non uniform behaviors. Static analysis of such a model was previously done in a data-flow oriented way, with type systems. This approach was based on constraint set resolution and was not able to deal with precise properties for communications of behaviors. We present here a new approach, control-flow oriented, based on the abstract interpretation framework, able to deal with communication of behaviors. Within our new analyses, we are able to verify most of the previous properties we observed as well as new ones, principally based on occurrence counting

From Single-thread to Multithreaded: An Efficient Static Analysis Algorithm

A great variety of static analyses that compute safety properties of single-thread programs have now been developed. This paper presents a systematic method to extend a class of such static analyses, so that they handle programs with multiple POSIX-style threads. Starting from a pragmatic operational semantics, we build a denotational semantics that expresses reasoning a la assume-guarantee. The final algorithm is then derived by abstract interpretation. It analyses each thread in turn, propagating interferences between threads, in addition to other semantic information. The combinatorial explosion, ensued from the explicit consideration of all interleavings, is thus avoided. The worst case complexity is only increased by a factor n compared to the single-thread case, where n is the number of instructions in the program. We have implemented prototype tools, demonstrating the practicality of the approach

Improving Strategies via SMT Solving

We consider the problem of computing numerical invariants of programs by abstract interpretation. Our method eschews two traditional sources of imprecision: (i) the use of widening operators for enforcing convergence within a finite number of iterations (ii) the use of merge operations (often, convex hulls) at the merge points of the control flow graph. It instead computes the least inductive invariant expressible in the domain at a restricted set of program points, and analyzes the rest of the code en bloc. We emphasize that we compute this inductive invariant precisely. For that we extend the strategy improvement algorithm of [Gawlitza and Seidl, 2007]. If we applied their method directly, we would have to solve an exponentially sized system of abstract semantic equations, resulting in memory exhaustion. Instead, we keep the system implicit and discover strategy improvements using SAT modulo real linear arithmetic (SMT). For evaluating strategies we use linear programming. Our algorithm has low polynomial space complexity and performs for contrived examples in the worst case exponentially many strategy improvement steps; this is unsurprising, since we show that the associated abstract reachability problem is Pi-p-2-complete