By Igor Walukiewicz (auth.), Roberto Amadio (eds.)
This publication constitutes the refereed court cases of the eleventh overseas convention on Foundations of software program technological know-how and Computational constructions, FOSSACS 2008, held in Budapest, Hungary, in March/April 2008 as a part of ETAPS 2008, the eu Joint meetings on conception and perform of Software.
The 33 revised complete papers awarded including the summary of one invited speak have been conscientiously reviewed and chosen from 124 submissions. A large number of theories and techniques to aid research, synthesis, transformation and verification of courses and software program platforms are addressed, together with the next subject matters: algebraic types, automata and language concept, behavioural equivalences, express types, computation techniques over discrete and non-stop info, limitless kingdom structures, computational constructions, logics of courses, modal, spatial, and temporal logics, types of concurrent, reactive, allotted, and cellular structures, strategy algebras and calculi, semantics of programming languages, software program specification and refinement, kind platforms and kind thought, basics of safety, semi-structured information, application correctness and verification.
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Extra info for Foundations of Software Science and Computational Structures: 11th International Conference, FOSSACS 2008, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2008, Budapest, Hungary, March 29 - April 6, 2008. Proceedi
In applications, the number of players may be much smaller than the size of the game graph. So it is interesting to know the complexity of the problem if the number of players is small. e. the number of non-matching bits. Clearly, if the number of players is bounded, then the Hamming distance of the thresholds can be bounded as well, but even if the number of players is not bounded, the distance of the thresholds may be. We show that, for games with parity winning conditions, NE retains the complexity of the classical parity game problem when restricted to payoﬀ thresholds of bounded Hamming distance: In general, the complexity goes down to UP ∩ co-UP, but for restricted classes of games we get membership in P.
20–34, 2008. c Springer-Verlag Berlin Heidelberg 2008 The Complexity of Nash Equilibria in Inﬁnite Multiplayer Games 21 of the system’s objective, so the environment is considered hostile. Therefore, traditionally, the research in this area has mostly looked at two-player games where each play is won by precisely one of the two players, so-called two-player zero-sum games. However, motivated by the modelling of distributed systems, interest in the general case has increased in recent years [3,4].
Lemma 3. For any strategy proﬁle σ and each player i ∈ Π, Pr(σ−i ,σi∗ ) (Wini ) = Prσ (Wini ) + Prσ (Wini ∩ Hiti ). The next lemma allows to infer the existence of a Nash equilibrium from the existence of a certain play. The proof uses so-called threat strategies (also known as trigger strategies), which are the basis of the folk theorems in the theory of repeated games (cf.  and [17, Chapter 8]). Lemma 4. If there exists a play π such that π ∈ Wini ∪ Hiti for each player i ∈ Π, then there exists a pure Nash equilibrium σ with π = σ .