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Interval Markov chains (IMCs) generalize ordinary Markov chains by having interval-valued transition probabilities. They are useful for modeling systems in which some transition probabilities depend on an unknown environment, are only approximately known, or are parameters that can be controlled. We consider the problem of computing values for the unknown… (More)

Verification of properties expressed in the two-variable fragment of first-order logic FO<sup>2</sup> has been investigated in a number of contexts. The satisfiability problem for FO<sup>2</sup> over arbitrary structures is known to be NEXPTIME-complete, with satisfiable formulas having exponential-sized models. Over words, where FO<sup>2</sup> is known to… (More)

Gipfeli is a high-speed compression algorithm that uses backward references with a 16-bit sliding window, based on 1977 paper by Lempel and Ziv, enriched with an ad-hoc entropy coding for both literals and backward references. We have implemented it in C++ and fine-tuned for very high performance. The compression ratio is similar to Zlib in the fastest… (More)

1 Erratum The authors would like to withdraw the claimed proof of Theorem 2 in the note below. The problems with the proof (and the overall approach, based on the notion of recurrent states) are detailed in a counterexample that can be found at

Verification of properties of first order logic with two variables FO 2 has been investigated in a number of contexts. Over arbitrary structures it is known to be decidable with NEXPTIME complexity, with finitely satisfiable formulas having exponential-sized models. Over word structures, where FO 2 is known to have the same expressiveness as unary temporal… (More)

Model checking linear-time properties expressed in first-order logic has non-elementary complexity, and thus various restricted logical languages are employed. In this paper we consider two such restricted specification logics, linear temporal logic (LTL) and two-variable first-order logic (FO 2). LTL is more expressive but FO 2 can be more succinct, and… (More)

In the last decade, the power of the state-of-the-art SAT and Integer Programming solvers has dramatically increased. They implement many new techniques and heuristics and since any NP problem can be converted to SAT or ILP instance, we could take advantage of these techniques in general by converting the instance of NP problem to SAT formula or Integer… (More)

ii Acknowledgements I am grateful to my supervisors James Worrell and Joël Ouaknine for the great topic and invaluable guidance, support, discussions and suggestions during my work on the dissertation. I would also like to thank Stephan Kreutzer a lot for guiding me through this master's program. Finally I appreciate Engineering and Physical Sciences… (More)

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