Derivation of Non-structural Invariants of Petri Nets Using Abstract Interpretation

Clarisó, Robert; Rodríguez-Carbonell, Enric; Cortadella, Jordi

doi:10.1007/11494744_12

Cited by 5 publications

(6 citation statements)

References 15 publications

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“…This matrix measures the amount of correlation between variables t i and t j : when |A(i, j)| ⋍ 1 then both variables are highly correlated. Finally, iii) the number of groups is decided by finding the eigenvalues and eigenvectors of A: the eigenvalues are sorted according to their value (the highest eigenvalue explains the highest correlation and so on), and only the most important (those that explain the important amount of correlation) are taken 6 . For each selected eigenvalue λ i , we can select the leader of the group for λ i by looking at the corresponding eigenvector α 1 · x 1 + .…”

Section: Identification Of Groups Of Tightly Coupled Eventsmentioning

confidence: 99%

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Process Mining Meets Abstract Interpretation

Carmona

Cortadella

2010

Lecture Notes in Computer Science

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Abstract. The discovery of process models out of system traces is a 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 this theory is Process Mining, an area that tries to incorporate the use of formal models both in the design and use of information systems.

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Section: Identification Of Groups Of Tightly Coupled Eventsmentioning

confidence: 99%

“…For example, some analysis based on abstract interpretation can discover numeric invariants among the variables of a program. Also, it has been applied to extract invariants from a PN [6]. Several abstract domains can be used to describe the invariants: intervals [7], octagons [13], convex polyhedra [9], among others.…”

Section: Introductionmentioning

confidence: 99%

Process Mining Meets Abstract Interpretation

Carmona

Cortadella

2010

Lecture Notes in Computer Science

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“…Whereas Colón's method can only consider equality tests, our method can handle both equality and disequality tests. This difference can be crucial in certain applications, like the analysis of Petri nets [5,27] and cache coherence protocols [15], as can be seen with the examples in Section 8.…”

Section: Related Workmentioning

confidence: 99%

“…The linear invariants produced by the linear invariant generator StInG[33], obtained by abstract interpretation with convex polyhedra and also by applying constraint-based invariant generation, do not suffice to prove the safety properties of the system either 5. These examples are available at www.lsi.upc.edu/~erodri .…”

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confidence: 99%

Automatic generation of polynomial invariants of bounded degree using abstract interpretation

Rodríguez-Carbonell

Kapur

2007

Science of Computer Programming

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A method for generating polynomial invariants of imperative programs is presented using the abstract interpretation framework. It is shown that for programs with polynomial assignments, an invariant consisting of a conjunction of polynomial equalities can be automatically generated for each program point. The proposed approach takes into account tests in conditional statements as well as in loops, insofar as they can be abstracted into polynomial equalities and disequalities. The semantics of each program statement is given as a transformation on polynomial ideals. Merging of execution paths is defined as the intersection of the polynomial ideals associated with each path. For loop junctions, a family of widening operators based on selecting polynomials up to a certain degree is proposed. The presented method has been implemented and successfully tried on many programs. Heuristics employed in the implementation to improve its efficiency are discussed, and tables providing details about its performance are included.

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“…In order to converge, this technique introduces a widening operator which result in weak invariant. In [2], R. Clarisó presented an approach to generate linear inequalities and polynomial equalities as invariant by using abstract interpretation.…”

Section: Introductionmentioning

confidence: 99%

Automated generation of algebraic invariants for Petri net

Zeng

Shan

2009

2009 IEEE International Conference on Control and Automation

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As one of mathematical representations of discrete distributed systems, Petri net has been widely used to model, analyze and simulate concurrent and distributed systems. The algebraic invariant is a powerful technique for the verification of Petri net. In this paper, we present a new and simple technique to construct the invariant of Petri net based on its properties. This technique can generate the invariant without computing DNF formula or Gröbner bases or using quantifier elimination, thereby circumventing difficulties in recent approaches. From the preliminary experiment results, the performance of this technique is significant.

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Derivation of Non-structural Invariants of Petri Nets Using Abstract Interpretation

Cited by 5 publications

References 15 publications

Process Mining Meets Abstract Interpretation

Process Mining Meets Abstract Interpretation

Automatic generation of polynomial invariants of bounded degree using abstract interpretation

Automated generation of algebraic invariants for Petri net

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