Transfer Function Synthesis without Quantifier Elimination

Traditionally, transfer functions have been designed manually for each operation in a program, instruction by instruction. In such a setting, a transfer function describes the semantics of a single instruction, detailing how a given abstract input state is mapped to an abstract output state. The net effect of a sequence of instructions, a basic block, can then be calculated by composing the transfer functions of the constituent instructions. However, precision can be improved by applying a single transfer function that captures the semantics of the block as a whole. Since blocks are program-dependent, this approach necessitates automation. There has thus been growing interest in computing transfer functions automatically, most notably using techniques based on quantifier elimination. Although conceptually elegant, quantifier elimination inevitably induces a computational bottleneck, which limits the applicability of these methods to small blocks. This paper contributes a method for calculating transfer functions that finesses quantifier elimination altogether, and can thus be seen as a response to this problem. The practicality of the method is demonstrated by generating transfer functions for input and output states that are described by linear template constraints, which include intervals and octagons.Comment: 37 pages, extended version of ESOP 2011 pape

Automatic modular abstractions for template numerical constraints

We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and containing linear assignments and tests. In addition to loop-free code, the same method also applies for obtaining least fixed points as functions of the precondition, which permits the analysis of loops and recursive functions. Our algorithms are based on new quantifier elimination and symbolic manipulation techniques. Given the specification of an abstract domain, and a program block, our method automatically outputs an implementation of the corresponding abstract transformer. It is thus a form of program transformation. The motivation of our work is data-flow synchronous programming languages, used for building control-command embedded systems, but it also applies to imperative and functional programming

Experiments with Automated Reasoning in the Class

International audienceThe European Erasmus+ project ARC-Automated Reasoning in the Class aims at improving the academic education in disciplines related to Computational Logic by using Automated Reasoning tools. We present the technical aspects of the tools as well as our education experiments, which took place mostly in virtual lectures due to the COVID pandemics. Our education goals are: to support the virtual interaction between teacher and students in the absence of the blackboard, to explain the basic Computational Logic algorithms, to study their implementation in certain programming environments, to reveal the main relationships between logic and programming, and to develop the proof skills of the students. For the introductory lectures we use some programs in C and in Mathematica in order to illustrate normal forms, resolution, and DPLL (Davis-Putnam-Logemann-Loveland) with its Chaff version, as well as an implementation of sequent calculus in the Theorema system. Furthermore we developed special tools for SAT (propositional satisfiability), some based on the original methods from the partners, including complex tools for SMT (Satisfiability Modulo Theories) that allow the illustration of various solving approaches. An SMT related approach is natural-style proving in Elementary Analysis, for which we developed and interesting set of practical heuristics. For more advanced lectures on rewrite systems we use the Coq programming and proving environment, in order on one hand to demonstrate programming in functional style and on the other hand to prove properties of programs. Other advanced approaches used in some lectures are the deduction based synthesis of algorithms and the techniques for program transformation

Tools and Algorithms for the Construction and Analysis of Systems

This open access two-volume set constitutes the proceedings of the 27th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2021, which was held during March 27 – April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The total of 41 full papers presented in the proceedings was carefully reviewed and selected from 141 submissions. The volume also contains 7 tool papers; 6 Tool Demo papers, 9 SV-Comp Competition Papers. The papers are organized in topical sections as follows: Part I: Game Theory; SMT Verification; Probabilities; Timed Systems; Neural Networks; Analysis of Network Communication. Part II: Verification Techniques (not SMT); Case Studies; Proof Generation/Validation; Tool Papers; Tool Demo Papers; SV-Comp Tool Competition Papers