Some Perspectives of Infinite-State Verification

2005 ◽  
pp. 3-10 ◽  
Author(s):  
Wolfgang Thomas
Keyword(s):  
Infinite State

Insensitivity of steady-state distributions of generalized semi-Markov processes by speeds

1978 ◽  
Vol 10 (04) ◽  
pp. 836-851 ◽  
Author(s):  
R. Schassberger
Keyword(s):  
Steady State ◽  
General System ◽  
State Distribution ◽  
Lifetime Distributions ◽  
State Dependent ◽  
Semi Markov Process ◽  
Semi Markov Processes ◽  
Infinite State ◽  
State Case ◽  
Residual Lifetimes

A generalized semi-Markov process with speeds describes the fluctuation, in time, of the state of a certain general system involving, at any given time, one or more living components, whose residual lifetimes are being reduced at state-dependent speeds. Conditions are given for the stationary state distribution, when it exists, to depend only on the means of some of the lifetime distributions, not their exact shapes. This generalizes results of König and Jansen, particularly to the infinite-state case.

scholarly journals Local model checking for infinite state spaces

1992 ◽  
Vol 96 (1) ◽  
pp. 157-174 ◽  
Author(s):  
Julian Bradfield ◽  
Colin Stirling
Keyword(s):  
Model Checking ◽  
Local Model ◽  
State Spaces ◽  
Infinite State ◽  
Local Model Checking

scholarly journals Model Completeness, Uniform Interpolants and Superposition Calculus

2021 ◽  
Author(s):  
Diego Calvanese ◽  
Silvio Ghilardi ◽  
Alessandro Gianola ◽  
Marco Montali ◽  
Andrey Rivkin
Keyword(s):  
Automated Reasoning ◽  
Quantifier Elimination ◽  
Effective Solution ◽  
Model Completeness ◽  
Present Contribution ◽  
First Order ◽  
Reduction Strategies ◽  
Infinite State Systems ◽  
Infinite State ◽  
Superposition Calculus

AbstractUniform interpolants have been largely studied in non-classical propositional logics since the nineties; a successive research line within the automated reasoning community investigated uniform quantifier-free interpolants (sometimes referred to as “covers”) in first-order theories. This further research line is motivated by the fact that uniform interpolants offer an effective solution to tackle quantifier elimination and symbol elimination problems, which are central in model checking infinite state systems. This was first pointed out in ESOP 2008 by Gulwani and Musuvathi, and then by the authors of the present contribution in the context of recent applications to the verification of data-aware processes. In this paper, we show how covers are strictly related to model completions, a well-known topic in model theory. We also investigate the computation of covers within the Superposition Calculus, by adopting a constrained version of the calculus and by defining appropriate settings and reduction strategies. In addition, we show that computing covers is computationally tractable for the fragment of the language used when tackling the verification of data-aware processes. This observation is confirmed by analyzing the preliminary results obtained using the mcmt tool to verify relevant examples of data-aware processes. These examples can be found in the last version of the tool distribution.

COMMENTS ON PIERCE’S DISCUSSION OF ‘FINITE VS. INFINITE STATE GRAMMARS’

Linguistics ◽  
1973 ◽  
Vol 11 (102) ◽  
Author(s):  
CHARLES R. PETERS
Keyword(s):  
Infinite State

scholarly journals Microcanonical Entropy of the Infinite-State Potts Model

2011 ◽  
Vol 2011 ◽  
pp. 1-5 ◽  
Author(s):  
Jonas Johansson ◽  
Mats-Erik Pistol
Keyword(s):  
Density Of States ◽  
Thermodynamic Limit ◽  
Potts Model ◽  
Direct Consequence ◽  
Configurational Energy ◽  
First Order ◽  
Entire Energy Range ◽  
Straight Line ◽  
First Order Transition ◽  
Infinite State

In this investigation we show that the entropy of the two-dimensional infinite-state Potts model is linear in configurational energy in the thermodynamic limit. This is a direct consequence of the local convexity of the microcanonical entropy, associated with a finite system undergoing a first-order transition. For a sufficiently large number of states , this convexity spans the entire energy range of the model. In the thermodynamic limit, the convexity becomes insignificant, and the microcanonical entropy (the logarithm of the density of states) tends to a straight line. In order to demonstrate the behaviour of the convexity, we use the Wang-Landau Monte-Carlo technique to numerically calculate the density of states for a few finite but high values of . Finally, we calculate the free energy and discuss the generality of our results.

scholarly journals Reachability Modulo Theory Library

10.29007/f3rp ◽  
2018 ◽  
Author(s):  
Francesco Alberti ◽  
Roberto Bruttomesso ◽  
Silvio Ghilardi ◽  
Silvio Ranise ◽  
Natasha Sharygina
Keyword(s):  
Reachability Analysis ◽  
Safety Properties ◽  
Standard Language ◽  
Transition Systems ◽  
Smt Solvers ◽  
Verification Tools ◽  
Infinite State Systems ◽  
Infinite State

Reachability analysis of infinite-state systems plays a central role in many verification tasks. In the last decade, SMT-Solvers have been exploited within many verification tools to discharge proof obligations arising from reachability analysis. Despite this, as of today there is no standard language to deal with transition systems specified in the SMT-LIB format. This paper is a first proposal for a new SMT-based verification language that is suitable for defining transition systems and safety properties.

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