Characterisation of the State Spaces of Live and Bounded Marked Graph Petri Nets

2014 ◽  
pp. 161-172 ◽  
Author(s):  
Eike Best ◽  
Raymond Devillers
Keyword(s):  
Petri Nets ◽  
The State ◽  
State Spaces ◽  
Marked Graph

scholarly journals Characterisation of the state spaces of marked graph Petri nets

2017 ◽  
Vol 253 ◽  
pp. 399-410 ◽  
Author(s):  
Eike Best ◽  
Raymond Devillers
Keyword(s):  
Petri Nets ◽  
The State ◽  
State Spaces ◽  
Marked Graph

scholarly journals Model Checking Coloured Petri Nets - Exploiting Strongly Connected Components

1997 ◽  
Vol 26 (519) ◽  
Author(s):  
Allan Cheng ◽  
Søren Christensen ◽  
Kjeld Høyer Mortensen
Keyword(s):  
Model Checking ◽  
Petri Nets ◽  
The State ◽  
Connected Components ◽  
Coloured Petri Nets ◽  
Transition Systems ◽  
Strongly Connected Components ◽  
State Spaces ◽  
Labelled Transition Systems ◽  
Strongly Connected

In this paper we present a CTL-like logic which is interpreted over the state spaces of Coloured Petri Nets. The logic has been designed to express properties of both state and transition information. This is possible because the state spaces are labelled transition systems. We compare the expressiveness of our logic with CTL's. Then, we present a model checking algorithm which for efficiency reasons utilises strongly connected components and formula reduction rules. We present empirical results for non-trivial examples and compare the performance of our algorithm with that of Clarke, Emerson, and Sistla.

scholarly journals Modular State Space Analysis of Coloured Petri Nets

1997 ◽  
Vol 26 (524) ◽  
Author(s):  
Søren Christensen ◽  
Laure Petrucci
Keyword(s):  
Petri Nets ◽  
State Space ◽  
The State ◽  
Total System ◽  
Entire System ◽  
State Spaces ◽  
Space Analysis ◽  
State Space Analysis ◽  
Full State ◽  
Local Properties

<p>State Space Analysis is one of the most developed analysis methods for Petri Nets. The main problem of state space analysis is the size of the state spaces. Several ways to reduce it have been proposed but cannot yet handle industrial size systems.</p><p>Large models often consist of a set of modules. Local properties of each module can be checked separately, before checking the validity of the entire system. We want to avoid the construction of a single state space of the entire system.</p><p>When considering transition sharing, the behaviour of the total system can be capture by the state spaces of modules combined with a Synchronisation Graph. To verify that we do not lose information we show how the full state space can be conctructed.</p><p>We show how it is possible to determine usual Petri Nets properites, without unfolding to the ordinary state space.</p>

Condensed State Spaces for Timed Petri Nets

2001 ◽  
pp. 101-120 ◽  
Author(s):  
Søren Christensen ◽  
Lars Michael Kristensen ◽  
Thomas Mailund
Keyword(s):  
Petri Nets ◽  
Condensed State ◽  
Timed Petri Nets ◽  
State Spaces

Conductance bounds on the L 2 convergence rate of Metropolis algorithms on unbounded state spaces

2004 ◽  
Vol 36 (01) ◽  
pp. 243-266
Author(s):  
Søren F. Jarner ◽  
Wai Kong Yuen
Keyword(s):  
Convergence Rate ◽  
Markov Chains ◽  
Spectral Gap ◽  
Unbounded Domains ◽  
Decomposition Theorem ◽  
Metropolis Algorithm ◽  
The State ◽  
Bounded Domains ◽  
Target Density ◽  
State Spaces

In this paper we derive bounds on the conductance and hence on the spectral gap of a Metropolis algorithm with a monotone, log-concave target density on an interval of ℝ. We show that the minimal conductance set has measure ½ and we use this characterization to bound the conductance in terms of the conductance of the algorithm restricted to a smaller domain. Whereas previous work on conductance has resulted in good bounds for Markov chains on bounded domains, this is the first conductance bound applicable to unbounded domains. We then show how this result can be combined with the state-decomposition theorem of Madras and Randall (2002) to bound the spectral gap of Metropolis algorithms with target distributions with monotone, log-concave tails on ℝ.

scholarly journals Well (and Better) Quasi-Ordered Transition Systems

2010 ◽  
Vol 16 (4) ◽  
pp. 457-515 ◽  
Author(s):  
Parosh Aziz Abdulla
Keyword(s):  
Petri Nets ◽  
Timed Automata ◽  
Timed Petri Nets ◽  
Transition Systems ◽  
State Spaces ◽  
Rewriting Systems ◽  
Symbolic Representations ◽  
Infinite State ◽  
Lossy Channel ◽  
Quasi Ordering

AbstractIn this paper, we give a step by step introduction to the theory ofwell quasi-orderedtransition systems. The framework combines two concepts, namely (i) transition systems which aremonotonicwrt. awell-quasi ordering; and (ii) a scheme for symbolicbackwardreachability analysis. We describe several models with infinite-state spaces, which can be analyzed within the framework, e.g., Petri nets, lossy channel systems, timed automata, timed Petri nets, and multiset rewriting systems. We will also presentbetter quasi-orderedtransition systems which allow the design of efficient symbolic representations of infinite sets of states.

Bounds for the Reliability of Multistate Systems with Partially Ordered State Spaces and Stochastically Monotone Markov Transitions

2003 ◽  
Vol 10 (03) ◽  
pp. 235-248
Author(s):  
Bo Henry Lindqvist
Keyword(s):  
Markov Chain ◽  
System Performance ◽  
Failure Time ◽  
The State ◽  
Upper And Lower Bounds ◽  
State Spaces ◽  
Partially Ordered ◽  
Perfect System ◽  
Multistate System ◽  
Ordered State

Consider a multistate system with partially ordered state space E, which is divided into a set C of working states and a set D of failure states. Let X(t) be the state of the system at time t and suppose {X(t)} is a stochastically monotone Markov chain on E. Let T be the failure time, i.e., the hitting time of the set D. We derive upper and lower bounds for the reliability of the system, defined as Pm(T > t) where m is the state of perfect system performance.

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