438 research outputs found
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Petri net equivalence
Determining whether two Petri nets are equivalent is an interesting problem from both practical and theoretical standpoints. Although it is undecidable in the general case, for many interesting nets the equivalence problem is solvable. This paper explores, mostly from a theoretical point of view, some of the issues of Petri net equivalence, including both reachability sets and languages. Some new definitions of reachability set equivalence are described which allow the markings of some places to be treated identically or ignored, analogous to the Petri net languages in which multiple transitions may be labeled with the same symbol or with the empty string. The complexity of some decidable Petri net equivalence problems is analyzed
Conformance checking: A state-of-the-art literature review
Conformance checking is a set of process mining functions that compare
process instances with a given process model. It identifies deviations between
the process instances' actual behaviour ("as-is") and its modelled behaviour
("to-be"). Especially in the context of analyzing compliance in organizations,
it is currently gaining momentum -- e.g. for auditors. Researchers have
proposed a variety of conformance checking techniques that are geared towards
certain process model notations or specific applications such as process model
evaluation. This article reviews a set of conformance checking techniques
described in 37 scholarly publications. It classifies the techniques along the
dimensions "modelling language", "algorithm type", "quality metric", and
"perspective" using a concept matrix so that the techniques can be better
accessed by practitioners and researchers. The matrix highlights the dimensions
where extant research concentrates and where blind spots exist. For instance,
process miners use declarative process modelling languages often, but
applications in conformance checking are rare. Likewise, process mining can
investigate process roles or process metrics such as duration, but conformance
checking techniques narrow on analyzing control-flow. Future research may
construct techniques that support these neglected approaches to conformance
checking
Calculating Colimits Compositionally
We show how finite limits and colimits can be calculated compositionally
using the algebras of spans and cospans, and give as an application a proof of
the Kleene Theorem on regular languages
Synchrony versus causality in distributed systems
Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Given a synchronous system, we study the question whether – or, under which conditions – the behaviour of that system can be realized by a (non-trivially) distributed and hence asynchronous implementation. In this paper, we partially answer this question by examining the role of causality for the implementation of synchrony in two fundamental different formalisms of concurrency, Petri nets and the π-calculus. For both formalisms it turns out that each ‘good’ encoding of synchronous interactions using just asynchronous interactions introduces causal dependencies in the translation
Verification and Parameter Synthesis for Real-Time Programs using Refinement of Trace Abstraction
We address the safety verification and synthesis problems for real-time
systems. We introduce real-time programs that are made of instructions that can
perform assignments to discrete and real-valued variables. They are general
enough to capture interesting classes of timed systems such as timed automata,
stopwatch automata, time(d) Petri nets and hybrid automata.
We propose a semi-algorithm using refinement of trace abstractions to solve
both the reachability verification problem and the parameter synthesis problem
for real-time programs.
All of the algorithms proposed have been implemented and we have conducted a
series of experiments, comparing the performance of our new approach to
state-of-the-art tools in classical reachability, robustness analysis and
parameter synthesis for timed systems. We show that our new method provides
solutions to problems which are unsolvable by the current state-of-the-art
tools
Synchrony versus causality in distributed systems
Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Given a synchronous system, we study the question whether – or, under which conditions – the behaviour of that system can be realized by a (non-trivially) distributed and hence asynchronous implementation. In this paper, we partially answer this question by examining the role of causality for the implementation of synchrony in two fundamental different formalisms of concurrency, Petri nets and the π-calculus. For both formalisms it turns out that each ‘good’ encoding of synchronous interactions using just asynchronous interactions introduces causal dependencies in the translation
A non-interleaving process calculus for multi-party synchronisation
We introduce the wire calculus. Its dynamic features are inspired by Milner's
CCS: a unary prefix operation, binary choice and a standard recursion
construct. Instead of an interleaving parallel composition operator there are
operators for synchronisation along a common boundary and non-communicating
parallel composition. The (operational) semantics is a labelled transition
system obtained with SOS rules. Bisimilarity is a congruence with respect to
the operators of the language. Quotienting terms by bisimilarity results in a
compact closed category
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