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

Deciding Conditional Termination

We address the problem of conditional termination, which is that of defining the set of initial configurations from which a given program always terminates. First we define the dual set, of initial configurations from which a non-terminating execution exists, as the greatest fixpoint of the function that maps a set of states into its pre-image with respect to the transition relation. This definition allows to compute the weakest non-termination precondition if at least one of the following holds: (i) the transition relation is deterministic, (ii) the descending Kleene sequence overapproximating the greatest fixpoint converges in finitely many steps, or (iii) the transition relation is well founded. We show that this is the case for two classes of relations, namely octagonal and finite monoid affine relations. Moreover, since the closed forms of these relations can be defined in Presburger arithmetic, we obtain the decidability of the termination problem for such loops.Comment: 61 pages, 6 figures, 2 table

Logahedra: A new weakly relational domain

Weakly relational numeric domains express restricted classes of linear inequalities that strike a balance between what can be described and what can be efficiently computed. Popular weakly relational domains such as bounded differences and octagons have found application in model checking and abstract interpretation. This paper introduces logahedra, which are more expressiveness than octagons, but less expressive than arbitrary systems of two variable per inequality constraints. Logahedra allow coefficients of inequalities to be powers of two whilst retaining many of the desirable algorithmic properties of octagons

Sparsity Preserving Algorithms for Octagons

Known algorithms for manipulating octagons do not preserve their sparsity, leading typically to quadratic or cubic time and space complexities even if no relation among variables is known when they are all bounded. In this paper, we present new algorithms, which use and return octagons represented as weakly closed difference bound matrices, preserve the sparsity of their input and have better performance in the case their inputs are sparse. We prove that these algorithms are as precise as the known ones

Modular Constraint Solver Cooperation via Abstract Interpretation

Cooperation among constraint solvers is difficult because different solving paradigms have different theoretical foundations. Recent works have shown that abstract interpretation can provide a unifying theory for various constraint solvers. In particular, it relies on abstract domains which capture constraint languages as ordered structures. The key insight of this paper is viewing cooperation schemes as abstract domains combinations. We propose a modular framework in which solvers and cooperation schemes can be seamlessly added and combined. This differs from existing approaches such as SMT where the cooperation scheme is usually fixed (e.g., Nelson-Oppen). We contribute to two new cooperation schemes: (i) interval propagators completion that allows abstract domains to exchange bound constraints, and (ii) delayed product which exchanges over-approximations of constraints between two abstract domains. Moreover, the delayed product is based on delayed goal of logic programming, and it shows that abstract domains can also capture control aspects of constraint solving. Finally, to achieve modularity, we propose the shared product to combine abstract domains and cooperation schemes. Our approach has been fully implemented, and we provide various examples on the flexible job shop scheduling problem. Under consideration for acceptance in TPLP.Comment: Paper presented at the 36th International Conference on Logic Programming (ICLP 2020), University Of Calabria, Rende (CS), Italy, September 2020, 17 pages. v2: Fix an example in Section 3.2 (improved closure

Vérification relationnelle pour des programmes avec des données entières

Les travaux présentés dans cette thèse sont lies aux problèmes de vérification de l'atteignabilité et de la terminaison de programmes qui manipulent des données entières non-bornées. On décrit une nouvelle méthode de vérification basée sur une technique d'accélération de boucle, qui calcule, de manière exacte, la clôture transitive d'une relation arithmétique. D'abord, on introduit un algorithme d'accélération de boucle qui peut calculer, en quelques secondes, des clôtures transitives pour des relations de l'ordre d'une centaine de variables. Ensuite, on présente une méthode d'analyse de l'atteignabilité, qui manipule des relations entre les variables entières d'un programme, et applique l'accélération pour le calcul des relations entrée-sortie des procédures, de façon modulaire. Une approche alternative pour l'analyse de l'atteignabilité, présentée également dans cette thèse, intègre l'accélération avec l'abstraction par prédicats, afin de traiter le problème de divergence de cette dernière. Ces deux méthodes ont été évaluées de manière pratique, sur un nombre important d'exemples, qui étaient, jusqu'a présent, hors de la portée des outils d'analyse existants. Dernièrement, on a étudié le problème de la terminaison pour certaines classes de boucles de programme, et on a montré la décidabilité pour les relations étudiées. Pour ces classes de relations arithmétiques, on présente un algorithme qui s'exécute en temps au plus polynomial, et qui calcule l'ensemble d'états qui peuvent générer une exécution infinie. Ensuite on a intégré cet algorithme dans une méthode d'analyse de la terminaison pour des programmes qui manipulent des données entières.This work presents novel methods for verification of reachability and termination properties of programs that manipulate unbounded integer data. Most of these methods are based on acceleration techniques which compute transitive closures of program loops. We first present an algorithm that accelerates several classes of integer relations and show that the new method performs up to four orders of magnitude better than the previous ones. On the theoretical side, our framework provides a common solution to the acceleration problem by proving that the considered classes of relations are periodic. Subsequently, we introduce a semi-algorithmic reachability analysis technique that tracks relations between variables of integer programs and applies the proposed acceleration algorithm to compute summaries of procedures in a modular way. Next, we present an alternative approach to reachability analysis that integrates predicate abstraction with our acceleration techniques to increase the likelihood of convergence of the algorithm. We evaluate these algorithms and show that they can handle a number of complex integer programs where previous approaches failed. Finally, we study the termination problem for several classes of program loops and show that it is decidable. Moreover, for some of these classes, we design a polynomial time algorithm that computes the exact set of program configurations from which non-terminating runs exist. We further integrate this algorithm into a semi-algorithmic method that analyzes termination of integer programs, and show that the resulting technique can verify termination properties of several non-trivial integer programs.SAVOIE-SCD - Bib.électronique (730659901) / SudocGRENOBLE1/INP-Bib.électronique (384210012) / SudocGRENOBLE2/3-Bib.électronique (384219901) / SudocSudocFranceF

Three-Dimensional Geometry Inference of Convex and Non-Convex Rooms using Spatial Room Impulse Responses

This thesis presents research focused on the problem of geometry inference for both convex- and non-convex-shaped rooms, through the analysis of spatial room impulse responses. Current geometry inference methods are only applicable to convex-shaped rooms, requiring between 6--78 discretely spaced measurement positions, and are only accurate under certain conditions, such as a first-order reflection for each boundary being identifiable across all, or some subset of, these measurements. This thesis proposes that by using compact microphone arrays capable of capturing spatiotemporal information, boundary locations, and hence room shape for both convex and non-convex cases, can be inferred, using only a sufficient number of measurement positions to ensure each boundary has a first-order reflection attributable to, and identifiable in, at least one measurement. To support this, three research areas are explored. Firstly, the accuracy of direction-of-arrival estimation for reflections in binaural room impulse responses is explored, using a state-of-the-art methodology based on binaural model fronted neural networks. This establishes whether a two-microphone array can produce accurate enough direction-of-arrival estimates for geometry inference. Secondly, a spherical microphone array based spatiotemporal decomposition workflow for analysing reflections in room impulse responses is explored. This establishes that simultaneously arriving reflections can be individually detected, relaxing constraints on measurement positions. Finally, a geometry inference method applicable to both convex and more complex non-convex shaped rooms is proposed. Therefore, this research expands the possible scenarios in which geometry inference can be successfully applied at a level of accuracy comparable to existing work, through the use of commonly used compact microphone arrays. Based on these results, future improvements to this approach are presented and discussed in detail

Object-oriented knowledge acquisition: Integrating construction of and reasoning in object-oriented knowledge bases

Päivikki Parpola presents in this research report the SeSKA (seamless structured knowledge acquisition) methodology, integrating phases of knowledge acquisition (KA) through seamless transformations between object-oriented (OO) models. This attacks the problem of disintegration, or the gap between phases. The methodology is accompanied by presentation of the SOOKAT (structured object-oriented knowledge acquisition) tool supporting it. SeSKA and SOOKAT extend the KA process to constructing knowledge bases by instantiating a series of models for inferencing. The models are constructed in SOOKAT utilizing metaobject protocols. Inferences performed in instantiations of OO models are guided by control objects (CO). Messages are sent between COs and components of the inference structure. A specific CO, possibly using subordinate COs, can be specified for each inference strategy. There exists a mutual CO for forward and backward chaining that can also be used when reasoning according to protocols. In addition, COs for problem-solving methods (PSMs), such as cover-and-differentiate or propose-and-revise, can be used.Three example applications are used for demonstrating the properties of the SeSKA methodology and SOOKAT, that is, a mineral classification "toy application", Sisyphus III rock classification and dietary management of multiple sclerosis.Mechanisms for importing problem-solving methods (PSMs) over the Internet, as well as for generating specific control objects (COs) for them, remain open to further development.  Päivikki Parpola (1965-2015) was a Ph.D. student at Aalto University. Her research interests concerned knowledge acquisition and presentation, development and reasoning in expert systems for different application fields, using the object-oriented paradigm. She received her M.Sc. in 1988 and Lic.Phil. in 1995 from the Department of Computer Science at the University of Helsinki. Her M.Sc. thesis concerned forming a formal grammar based on text samples of natural language or unknown writing. Research presented in her Lic.Phil. thesis continued in her Ph.D. studies. She worked with Nokia Research Center from 1987 to 1993. In addition to her thesis, she published multiple international and domestic conference papers and articles as well as contributed in European Union research project publications