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Nets with tokens which carry data
 In Proc. 28th International Conference on Application and Theory of Petri Nets (ICATPN’07), volume 4546 of Lecture Notes in Computer Science
, 2007
"... Abstract. We study data nets, a generalisation of Petri nets in which tokens carry data from linearlyordered infinite domains and in which wholeplace operations such as resets and transfers are possible. Data nets subsume several known classes of infinitestate systems, including multiset rewritin ..."
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Cited by 32 (2 self)
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Abstract. We study data nets, a generalisation of Petri nets in which tokens carry data from linearlyordered infinite domains and in which wholeplace operations such as resets and transfers are possible. Data nets subsume several known classes of infinitestate systems, including multiset rewriting systems and polymorphic systems with arrays. We show that coverability and termination are decidable for arbitrary data nets, and that boundedness is decidable for data nets in which wholeplace operations are restricted to transfers. By providing an encoding of lossy channel systems into data nets without wholeplace operations, we establish that coverability, termination and boundedness for the latter class have nonprimitive recursive complexity. The main result of the paper is that, even for unordered data domains (i.e., with only the equality predicate), each of the three verification problems for data nets without wholeplace operations has nonelementary complexity. 1
Symbolic Model Checking of InfiniteState Systems Using Narrowing
"... Rewriting is a general and expressive way of specifying concurrent systems, where concurrent transitions are axiomatized by rewrite rules. Narrowing is a complete symbolic method for model checking reachability properties. We show that this method can be reinterpreted as a lifting simulation relatin ..."
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Cited by 24 (12 self)
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Rewriting is a general and expressive way of specifying concurrent systems, where concurrent transitions are axiomatized by rewrite rules. Narrowing is a complete symbolic method for model checking reachability properties. We show that this method can be reinterpreted as a lifting simulation relating the original system and the symbolic system associated to the narrowing transitions. Since the narrowing graph can be infinite, this lifting simulation only gives us a semidecision procedure for the failure of invariants. However, we propose new methods for folding the narrowing tree that can in practice result in finite systems that symbolically simulate the original system and can be used to algorithmically verify its properties. We also show how both narrowing and folding can be used to symbolically model check systems which, in addition, have state predicates, and therefore correspond to Kripke structures on which ACTL∗ and LTL formulas can be algorithmically verified using such finite symbolic abstractions.
The Model Results Technique Future Work References Gap Clauses/Constraints Def: positive Gap Constraints∧
, 2013
"... x − y ≥ k where x, y are integer variables or constants and k ∈ Z. positive GC are not negationclosed! Write Var = {x, y,...} for the variables Const ⊂ Z for the constants and Val for the set of valuations ν: Var → Z. ..."
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x − y ≥ k where x, y are integer variables or constants and k ∈ Z. positive GC are not negationclosed! Write Var = {x, y,...} for the variables Const ⊂ Z for the constants and Val for the set of valuations ν: Var → Z.
IOS Press Nets with tokens which carry data
"... Abstract. We study data nets, a generalisation of Petri nets in which tokens carry data from linearlyordered infinite domains and in which wholeplace operations such as resets and transfers are possible. Data nets subsume several known classes of infinitestate systems, including multiset rewriting ..."
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Abstract. We study data nets, a generalisation of Petri nets in which tokens carry data from linearlyordered infinite domains and in which wholeplace operations such as resets and transfers are possible. Data nets subsume several known classes of infinitestate systems, including multiset rewriting systems and polymorphic systems with arrays. We show that coverability and termination are decidable for arbitrary data nets, and that boundedness is decidable for data nets in which wholeplace operations are restricted to transfers. By providing an encoding of lossy channel systems into data nets without wholeplace operations, we establish that coverability, termination and boundedness for the latter class have nonprimitive recursive complexity. The main result of the paper is that, even for unordered data domains (i.e., with only the equality predicate), each of the three verification problems for data nets without wholeplace operations has nonelementary complexity. Keywords: Petri nets, infinitestate systems, program verification, computational complexity
AVIS 2006 Preliminary Version On the Coverability Problem for Constrained Multiset Rewriting
"... We investigate model checking of a computation model called Constrained Multiset Rewriting Systems (CMRS). A CMRS operates on configurations which are multisets of monadic predicate symbols, each with an argument ranging over the natural numbers. The transition relation is defined by a finite set of ..."
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We investigate model checking of a computation model called Constrained Multiset Rewriting Systems (CMRS). A CMRS operates on configurations which are multisets of monadic predicate symbols, each with an argument ranging over the natural numbers. The transition relation is defined by a finite set of rewriting rules which are conditioned by simple inequalities on variables and constants. This model is able to specify systems with an arbitrary number of components where the internal state of a component may contain values ranging over the natural numbers. In this paper we prove decidability of the coverability problem for CMRS. The algorithm is obtained by a nontrivial application of a methodology based on the theory of well and betterquasi orderings. We report on using a prototype implementation to verify parameterized versions of a mutual exclusion and an authentication protocol. Key words: Infinite state systems, Symbolic Verification
Depth boundedness in multiset rewriting systems with name binding
, 2010
"... In this paper we consider νMSR, a formalism that combines the two main existing approaches for multiset rewriting, namely MSR and CMRS. In νMSR we rewrite multisets of atomic formulae, in which some names may be restricted. νMSR are Turing complete. In particular, a very straightforward encodin ..."
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In this paper we consider νMSR, a formalism that combines the two main existing approaches for multiset rewriting, namely MSR and CMRS. In νMSR we rewrite multisets of atomic formulae, in which some names may be restricted. νMSR are Turing complete. In particular, a very straightforward encoding of πcalculus process can be done. Moreover, pνPN, an extension of Petri nets in which tokens are tuples of pure names, are equivalent to νMSR. We know that the monadic subclass of νMSR is a Well Structured Transition System. Here we prove that depthbounded νMSR, that is, νMSR systems for which the interdependance of names is bounded, are also Well Structured, by following the analogous steps to those followed by R. Meyer in the case of the πcalculus. As a corollary, also depthbounded pνPN are WSTS, so that coverability is decidable for them.