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1

Modelling and Simulation of Quantum Teleportation and Dense Coding Using Predicate/Transition-Nets

Varpaaniemi K., Ojala L.

Fundamenta Informaticae

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2008

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Vol. 85, nr 1-4

465-479

EN

Reachability analysis is one of the most successful methods used in design and validation of protocols for classical communication, whereas the predicate/transition-net formalism is one of the most appropriate formalisms for reachability analysis oriented modelling. Quantum teleportation and dense coding are non-classical communication protocols that have been widely researched in the field of quantum computing. In this article, we present predicate/transition-net models of these two protocols and use the PROD reachability analysis tool for analysing the models.

2

Towards Ambitious Approximation Algorithms in Stubborn Set Optimization

Varpaaniemi K.

Fundamenta Informaticae

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2003

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Vol. 54, nr 2,3

279-294

EN

This article continues research on the stubborn set method that constructs on-the-fly a reduced LTS that is CFFD-equivalent to the parallel composition of given LTSs. In particular, minimization of the number of successor states of a given state is reconsidered. The earlier suggested and/or-graph approach requires solving #P-complete counting problems in order to get the weights for the vertices of the and/or-graph. The ``branch-and-bound'' decision problem corresponding to the minimization of the sum of the computed weights is ``only'' NP-complete. Unfortunately, #P-complete counting does not seem easily avoidable in the general case because it is PP-complete to check whether a given stubborn set produces at most as many successor states as another given stubborn set. Instead of solving each of the subproblems, one could think of computing approximate solutions in such a way that the total effect of the approximations is a useful approximation itself.

3

Minimizing the Number of Successor States in the Stubborn Set Method

Varpaaniemi K.

Fundamenta Informaticae

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2002

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Vol. 51, nr 1,2

215-234

EN

Combinatorial explosion which occurs in parallel compositions of LTSs can be alleviated by letting the stubborn set method construct on-the-fly a reduced LTS that is CFFD- or CSP-equivalent to the actual parallel composition. This article considers the problem of minimizing the number of successor states of a given state in the reduced LTS. The problem can be solved by constructing an and/or-graph with weighted vertices and by finding a set of vertices that satisfies a certain constraint such that no set of vertices satisfying the constraint has a smaller sum of weights. Without weights, the and/or-graph can be constructed in low-degree polynomial time w.r.t. the length of the input of the problem. However, since actions can be nondeterministic and transitions can share target states, it is not known whether the weights are generally computable in polynomial time. Consequently, it is an open problem whether minimizing the number of successor states is as ``easy'' as minimizing the number of successor transitions.

4

Stable models for stubborn sets

Varpaaniemi K.

Fundamenta Informaticae

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2000

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Vol. 43, Nr 1-4

355-375

EN

The stubborn set method is one of the methods that try to relieve the state space explosion problem that occurs in state space generation. Spending some time in looking for "good'" stubborn sets can pay off in the total time spent in generating a reduced state space. This article shows how the method can exploit tools that solve certain problems of logic programs. The restriction of a definition of stubbornness to a given state can be translated into a variable-free logic program. When a stubborn set satisfying additional constraints is wanted, the additional constraints should be translated, too. It is easy to make the translation in such a way that each acceptable stubborn set of the state is represented by at least one stable model of the program, each stable model of the program represents at least one acceptable stubborn set of the state, and for each pair in the representation relation, the number of certain atoms in the stable model is equal to the number of enabled transitions of the represented stubborn set. So, in order to find a stubborn set which is good w.r.t. the number of enabled transitions, it suffices to find a stable model which is good w.r.t. the number of certain atoms. The article also presents a new NP-completeness result concerning stubborn sets.