Towards the Formal Specification and Verification of Maple Programs

In this paper, we present our ongoing work and initial results on the formal specification and verification of MiniMaple (a substantial subset of Maple with slight extensions) programs. The main goal of our work is to find behavioral errors in such programs w.r.t. their specifications by static analysis. This task is more complex for widely used computer algebra languages like Maple as these are fundamentally different from classical languages: they support non-standard types of objects such as symbols, unevaluated expressions and polynomials and require abstract computer algebraic concepts and objects such as rings and orderings etc. As a starting point we have defined and formalized a syntax, semantics, type system and specification language for MiniMaple

Termination of Triangular Integer Loops is Decidable

We consider the problem whether termination of affine integer loops is decidable. Since Tiwari conjectured decidability in 2004, only special cases have been solved. We complement this work by proving decidability for the case that the update matrix is triangular.Comment: Full version (with proofs) of a paper published in the Proceedings of the 31st International Conference on Computer Aided Verification (CAV '19), New York, NY, USA, Lecture Notes in Computer Science, Springer-Verlag, 201

Lifting CDCL to template-based abstract domains for program verification

The success of Conflict Driven Clause Learning (CDCL) for Boolean satisfiability has inspired adoption in other domains. We present a novel lifting of CDCL to program analysis called Abstract Conflict Driven Learning for Programs (ACDLP). ACDLP alternates between model search, which performs over-approximate deduction with constraint propagation, and conflict analysis, which performs under-approximate abduction with heuristic choice. We instantiate the model search and conflict analysis algorithms with an abstract domain of template polyhedra, strictly generalizing CDCL from the Boolean lattice to a richer lattice structure. Our template polyhedra can express intervals, octagons and restricted polyhedral constraints over program variables. We have implemented ACDLP for automatic bounded safety verification of C programs. We evaluate the performance of our analyser by comparing with CBMC, which uses Boolean CDCL, and Astrée, a commercial abstract interpretation tool. We observe two orders of magnitude reduction in the number of decisions, propagations, and conflicts as well as a 1.5x speedup in runtime compared to CBMC. Compared to Astrée, ACDLP solves twice as many benchmarks and has much higher precision. This is the first instantiation of CDCL with a template polyhedra abstract domain

Proving Safety with Trace Automata and Bounded Model Checking

Loop under-approximation is a technique that enriches C programs with additional branches that represent the effect of a (limited) range of loop iterations. While this technique can speed up the detection of bugs significantly, it introduces redundant execution traces which may complicate the verification of the program. This holds particularly true for verification tools based on Bounded Model Checking, which incorporate simplistic heuristics to determine whether all feasible iterations of a loop have been considered. We present a technique that uses \emph{trace automata} to eliminate redundant executions after performing loop acceleration. The method reduces the diameter of the program under analysis, which is in certain cases sufficient to allow a safety proof using Bounded Model Checking. Our transformation is precise---it does not introduce false positives, nor does it mask any errors. We have implemented the analysis as a source-to-source transformation, and present experimental results showing the applicability of the technique

Interpolation Properties and SAT-based Model Checking

Craig interpolation is a widespread method in verification, with important applications such as Predicate Abstraction, CounterExample Guided Abstraction Refinement and Lazy Abstraction With Interpolants. Most state-of-the-art model checking techniques based on interpolation require collections of interpolants to satisfy particular properties, to which we refer as "collectives"; they do not hold in general for all interpolation systems and have to be established for each particular system and verification environment. Nevertheless, no systematic approach exists that correlates the individual interpolation systems and compares the necessary collectives. This paper proposes a uniform framework, which encompasses (and generalizes) the most common collectives exploited in verification. We use it for a systematic study of the collectives and of the constraints they pose on propositional interpolation systems used in SAT-based model checking

Enhancement of the pasting properties of teff and maize starches through wet-heat processing with added stearic acid

This study determined the effects of stearic acid on the functional properties of teff 27 starch, a compound granule starch in comparison to maize, a simple type granule starch. 28 Stearic acid was incorporated into teff and maize starches and pasted (held for 5 or 120 29 min at 91°C) with an RVA (Rapid Visco Analyser). Teff starch with added stearic acid 30 (0.25 and 1.5% starch basis) did not produce a pasting peak viscosity within short 31 holding time (5 min) compared to maize starch. The paste viscosity of both teff and 32 maize starches with stearic acid increased to about three times with long pasting (120 33 min). This increase in paste viscosity occurred earlier for teff starch than maize starch. 34 Teff starch with stearic acid was more viscous and was non-gelling. Confocal laser 35 scanning microscopy showed that stearic acid did not diffuse in teff starch granules, but 36 seemed to coat them. However, stearic acid diffused inside maize starch granule through 37 channels. This microstructural difference may explain the different pasting behavior. 38 The early high paste viscosity and non gelling properties of the teff starch modified with 39 stearic acid could have promising applications in foods for example better mouthfeel 40 with lower starch concentration.The National Research Foundation of South Africa, Research Development funds from the University of Pretoria and the Maize Trust of South Africa for Ms TV D’Silva's bursary.http://www.elsevier.com/locate/jcsnf201

Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar

This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service for first-order automated reasoning. The main differences to SystemOnTPTP are the use of the Mizar language that is oriented towards human mathematicians (rather than the pure first-order logic used in SystemOnTPTP), and setting the service in the context of the large Mizar Mathematical Library of previous theorems,definitions, and proofs (rather than the isolated problems that are solved in SystemOnTPTP). These differences poses new challenges and new opportunities for automated reasoning and for proof presentation tools. This paper describes the overall structure of MizAR, and presents the automated reasoning systems and proof presentation tools that are combined to make MizAR a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial Intelligence and Symbolic Computation AISC 201

Checking bounded reachability in asynchronous systems by symbolic event tracing

This report presents a new symbolic technique for checking reachability properties of asynchronous systems by reducing the problem to satisfiability in restrained difference logic. The analysis is bounded by fixing a finite set of potential events, each of which may occur at most once in any order. The events are specified using high-level Petri nets. The logic encoding describes the space of possible causal links between events rather than possible sequences of states as in Bounded Model Checking. Independence between events is exploited intrinsically without partial order reductions, and the handling of data is symbolic. On a family of benchmarks, the proposed approach is consistently faster than Bounded Model Checking. In addition, this report presents a compact encoding of the restrained subset of difference logic in propositional logic

A Constraint Solver based on Abstract Domains

International audienceIn this article, we apply techniques from Abstract Interpretation (a general theory of semantic abstractions) to Constraint Programming (which aims at solving hard combinatorial problems with a generic framework based on first-order logics). We highlight some links and differences between these fields: both compute fixpoints by iteration but employ different extrapolation and refinement strategies; moreover, consistencies in Constraint Programming can be mapped to non-relational abstract domains. We then use these correspondences to build an abstract constraint solver that leverages abstract interpretation techniques (such as relational domains) to go beyond classic solvers. We present encouraging experimental results obtained with our prototype implementation

Building Better Bit-Blasting for Floating-Point Problems

An effective approach to handling the theory of floating-point is to reduce it to the theory of bit-vectors. Implementing the required encodings is complex, error prone and requires a deep understanding of floating-point hardware. This paper presents SymFPU, a library of encodings that can be included in solvers. It also includes a verification argument for its correctness, and experimental results showing that its use in CVC4 out-performs all previous tools. As well as a significantly improved performance and correctness, it is hoped this will give a simple route to add support for the theory of floating-point