Comparison Petri Nets - Finite State Automaton

2016 ◽  
pp. 25-33
Author(s):  
Jean-François Aubry ◽  
Nicolae Brinzei ◽  
Mohammed-Habib Mazouni
Keyword(s):  
Petri Nets ◽  
Finite State Automaton ◽  
Finite State

scholarly journals Formalization, Implementation, and Modeling of Institutional Controllers for Distributed Robotic Systems

2014 ◽  
Vol 20 (1) ◽  
pp. 127-141 ◽  
Author(s):  
José N. Pereira ◽  
Porfírio Silva ◽  
Pedro U. Lima ◽  
Alcherio Martinoli
Keyword(s):  
Petri Nets ◽  
Institutional Economics ◽  
Formal Model ◽  
Finite State Automaton ◽  
Robot Swarm ◽  
Design Program ◽  
Finite State ◽  
Generalized Stochastic Petri Net ◽  
Distributed Robotic System

The work described is part of a long term program of introducing institutional robotics, a novel framework for the coordination of robot teams that stems from institutional economics concepts. Under the framework, institutions are cumulative sets of persistent artificial modifications made to the environment or to the internal mechanisms of a subset of agents, thought to be functional for the collective order. In this article we introduce a formal model of institutional controllers based on Petri nets. We define executable Petri nets—an extension of Petri nets that takes into account robot actions and sensing—to design, program, and execute institutional controllers. We use a generalized stochastic Petri net view of the robot team controlled by the institutional controllers to model and analyze the stochastic performance of the resulting distributed robotic system. The ability of our formalism to replicate results obtained using other approaches is assessed through realistic simulations of up to 40 e-puck robots. In particular, we model a robot swarm and its institutional controller with the goal of maintaining wireless connectivity, and successfully compare our model predictions and simulation results with previously reported results, obtained by using finite state automaton models and controllers.

Soundness Verification of Data-Aware Process Models with Variable-to-Variable Conditions

2021 ◽  
Vol 182 (1) ◽  
pp. 1-29
Author(s):  
Paolo Felli ◽  
Massimiliano de Leoni ◽  
Marco Montali
Keyword(s):  
Petri Nets ◽  
Business Process ◽  
Control Flow ◽  
Finite State Automaton ◽  
Complex Data ◽  
Specific Class ◽  
Variable Operator ◽  
Constraint Graph ◽  
Model Complex ◽  
Finite State

Traditionally Business Process Modeling has only focused on the control-flow perspective, thus allowing process designers to specify the constraints on the activities of the process: the order and potential concurrency of their execution, their mutual exclusivity, the possibility of being repeated, etc. However, activities are executed by different resources, manipulate data objects and are constrained by the state of such objects. This requires that the traditional notion of soundness, typically introduced for control-flow-only models, is extended so as to consider data. Intuitively, a (data-aware) process model is sound if (1) it does not contain deadlocks, (2) no more activities are enabled when the process instance is marked as completed and finally (3) there are no parts of the model that cannot be executed. Although several data-aware notations have been introduced in the literature, not all of these are given a formal semantics. In this paper, we propose a technique for checking the data-aware soundness for a specific class of such integrated models, with a simple syntax and semantics, building on Data Petri Nets (DPNs). These are Petri nets enriched with case variables, where transitions are guarded by formulas that inspect and update such variables, and are of the form variable-operator-variable or variable-operator-constant. Even though DPNs are less expressive than Petri nets where data are carried by tokens, they elegantly capture business processes operating over simple case data, allowing to model complex data-aware decisions. We show that, if a DPN is data-aware sound, the Constraint Graph is a finite-state automaton; however, a finite-state Constraint Graph does not guarantee data-aware soundness, but provides a finite structure through which this property can be checked. Finally, we investigate further properties beyond data-aware soundness, such as the problem of verifying that an actor participating in the business process can unilaterally enforce data-aware soundness by restricting the possible executions of a bounded DPN, assuming this actor to be able to control the firing of some transitions and decide the value of some of the case variables whenever these are updated.

scholarly journals Combable functions, quasimorphisms, and the central limit theorem

2009 ◽  
Vol 30 (5) ◽  
pp. 1343-1369 ◽  
Author(s):  
DANNY CALEGARI ◽  
KOJI FUJIWARA
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Word Length ◽  
Hyperbolic Groups ◽  
Finite State Automaton ◽  
List Type ◽  
Generating Sets ◽  
Finite State ◽  
Word Hyperbolic Groups

AbstractA function on a discrete group is weakly combable if its discrete derivative with respect to a combing can be calculated by a finite-state automaton. A weakly combable function is bicombable if it is Lipschitz in both the left- and right-invariant word metrics. Examples of bicombable functions on word-hyperbolic groups include:(1)homomorphisms to ℤ;(2)word length with respect to a finite generating set;(3)most known explicit constructions of quasimorphisms (e.g. the Epstein–Fujiwara counting quasimorphisms).We show that bicombable functions on word-hyperbolic groups satisfy acentral limit theorem: if$\overline {\phi }_n$is the value of ϕ on a random element of word lengthn(in a certain sense), there areEandσfor which there is convergence in the sense of distribution$n^{-1/2}(\overline {\phi }_n - nE) \to N(0,\sigma )$, whereN(0,σ) denotes the normal distribution with standard deviationσ. As a corollary, we show that ifS1andS2are any two finite generating sets forG, there is an algebraic numberλ1,2depending onS1andS2such that almost every word of lengthnin theS1metric has word lengthn⋅λ1,2in theS2metric, with error of size$O(\sqrt {n})$.

scholarly journals Model Checking Temporal Logic Formulas Using Sticker Automata

2017 ◽  
Vol 2017 ◽  
pp. 1-33 ◽  
Author(s):  
Weijun Zhu ◽  
Changwei Feng ◽  
Huanmei Wu
Keyword(s):  
Model Checking ◽  
Temporal Logic ◽  
Complex Problem ◽  
Finite State Automaton ◽  
Dna Molecules ◽  
Single Stranded Dna ◽  
Finite State ◽  
Input Strings ◽  
Logic Model Checking ◽  
The Given

As an important complex problem, the temporal logic model checking problem is still far from being fully resolved under the circumstance of DNA computing, especially Computation Tree Logic (CTL), Interval Temporal Logic (ITL), and Projection Temporal Logic (PTL), because there is still a lack of approaches for DNA model checking. To address this challenge, a model checking method is proposed for checking the basic formulas in the above three temporal logic types with DNA molecules. First, one-type single-stranded DNA molecules are employed to encode the Finite State Automaton (FSA) model of the given basic formula so that a sticker automaton is obtained. On the other hand, other single-stranded DNA molecules are employed to encode the given system model so that the input strings of the sticker automaton are obtained. Next, a series of biochemical reactions are conducted between the above two types of single-stranded DNA molecules. It can then be decided whether the system satisfies the formula or not. As a result, we have developed a DNA-based approach for checking all the basic formulas of CTL, ITL, and PTL. The simulated results demonstrate the effectiveness of the new method.

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