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

Polyhedral Analysis using Parametric Objectives

The abstract domain of polyhedra lies at the heart of many program analysis techniques. However, its operations can be expensive, precluding their application to polyhedra that involve many variables. This paper describes a new approach to computing polyhedral domain operations. The core of this approach is an algorithm to calculate variable elimination (projection) based on parametric linear programming. The algorithm enumerates only non-redundant inequalities of the projection space, hence permits anytime approximation of the output

Interval Slopes as Numerical Abstract Domain for Floating-Point Variables

The design of embedded control systems is mainly done with model-based tools such as Matlab/Simulink. Numerical simulation is the central technique of development and verification of such tools. Floating-point arithmetic, that is well-known to only provide approximated results, is omnipresent in this activity. In order to validate the behaviors of numerical simulations using abstract interpretation-based static analysis, we present, theoretically and with experiments, a new partially relational abstract domain dedicated to floating-point variables. It comes from interval expansion of non-linear functions using slopes and it is able to mimic all the behaviors of the floating-point arithmetic. Hence it is adapted to prove the absence of run-time errors or to analyze the numerical precision of embedded control systems

Process mining meets abstract interpretation

The discovery of process models out of system traces is an interesting problem that has received significant attention in the last years. In this work, a theory for the derivation of a Petri net from a set of traces is presented. The method is based on the theory of abstract interpretation, which has been applied successfully in other areas. The principal application of the theory presented is Process Mining, an area that tries to incorporate the use of formal models both in the design and use of information systems.Postprint (published version

Behavioral cartography of timed automata

Abstract. We aim at finding a set of timing parameters for which a given timed automaton has a “good ” behavior. We present here a novel approach based on the decomposition of the parametric space into behavioral tiles, i.e., sets of parameter valuations for which the behavior of the system is uniform. This gives us a behavioral cartography according to the values of the parameters. It is then straightforward to partition the space into a “good ” and a “bad ” subspace, according to the behavior of the tiles. We extend this method to probabilistic systems, allowing to decompose the parametric space into tiles for which the minimal (resp. maximal) probability of reaching a given location is uniform. An implementation has been made, and experiments successfully conducted.

IMITATOR: A tool for synthesizing constraints on timing bounds of timed automata

Abstract. We present here Imitator, a tool for synthesizing constraints on timing bounds (seen as parameters) in the framework of timed automata. Unlike classical synthesis methods, we take advantage of a given reference valuation of the parameters for which the system is known to behave properly. Our aim is to generate a constraint such that, under any valuation satisfying this constraint, the system is guaranteed to behave, in terms of alternating sequences of locations and actions, as under the reference valuation. This is useful for safely relaxing some values of the reference valuation, and optimizing timing bounds of the system. We have successfully applied our tool to various examples of asynchronous circuits and protocols.

Lignin-degrading peroxidases from genome of selective ligninolytic fungusCeriporiopsis subvermispora.

Abstract. We present a method for generating linear invariants for domain consisting of arbitrary polyhedra of a predefined fixed shape. The basic operations on the domain like abstraction, intersection, join and inclusion tests are all posed as linear optimization queries, which can be solved efficiently by existing LP solvers. The number and dimensionality of the LP queries are polynomial in the program dimensionality, size and the number of target invariants. The method generalizes similar analyses in the interval, octagon, and octahedra domains, without resorting to polyhedral manipulations. We demonstrate the performance of our method on some benchmark programs.

Widening operators for weakly-relational numeric abstractions

Abstract. We discuss the construction of proper widening operators on several weakly-relational numeric abstractions. Our proposal differs domains, whose elements are geometric shapes, instead of the (more concrete) syntactic abstract domains of constraint networks and matrices. Since the closure by entailment operator preserves geometric shapes, but not their syntactic expressions, our widenings are immune from the divergence issues that could be faced by the previous approaches when interleaving the applications of widening and closure. The new widenings, which are variations of the standard widening for convex polyhedra defined by Cousot and Halbwachs, can be made as precise as the previous proposals working on the syntactic domains. The implementation of each new widening relies on the availability of an effective reduction procedure for the considered constraint description: we provide such an algorithm for the domain of octagonal shapes.

Heuristic mining revamped : an interactive, data-aware, and conformance-aware miner

Process discovery methods automatically infer process models based on events logs that are recorded by information systems. Several heuristic process discovery methods have been proposed to cope with less structured processes and the presence of noise in the event log. However, (1) a large parameter space needs to be explored, (2) several of the many available heuristics can be chosen from, (3) data attributes are not used for discovery, (4) discovered models are not visualized as described in literature, and (5) existing tools do not give reliable quality diagnostics for discovered models. We present the interactive Data-aware Heuristics Miner (iDHM), a modular tool that attempts to address those five issues. The iDHM enables quick interactive exploration of the parameter space and several heuristics. It uses data attributes to improve the discovery procedure and provides built-in conformance checking to get direct feedback on the quality of the model. It is the first tool that visualizes models using the concise Causal Net (C-Net) notation. We provide a walk-through of the iDHM by applying it to a large event log with hospital billing information