Dagstuhl Seminar Proceedings, Volume 8271
Dagstuhl Seminar Proceedings
DagSemProc
https://www.dagstuhl.de/dagpub/1862-4405
https://dblp.org/db/series/dagstuhl
1862-4405
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
8271
2008
https://drops.dagstuhl.de/entities/volume/DagSemProc-volume-8271
08271 Abstracts Collection – Topological and Game-Theoretic Aspects of Infinite Computations
From June 29, 2008, to July 4, 2008, the Dagstuhl Seminar 08271 ``Topological and Game-Theoretic Aspects of Infinite Computations'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, many participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
Automata theory
computability in analysis
dataflow computation
hierarchies
infinite computations
infinite games
reactive systems
specification and verification
topological complexity
Wadge reducibility
1-17
Regular Paper
Peter
Hertling
Peter Hertling
Victor
Selivanov
Victor Selivanov
Wolfgang
Thomas
Wolfgang Thomas
William W.
Wadge
William W. Wadge
Klaus
Wagner
Klaus Wagner
10.4230/DagSemProc.08271.1
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08271 Executive Summary – Topological and Game-Theoretic Aspects of Infinite Computations
The theory of the infinite behaviour of continuously operating computing devices is of primary importance for several branches of theoretical and practical computer science. In particular, it is fundamental for the verification and synthesis of reactive systems like microprocessors or operating systems, for the understanding of dataflow computation, and for the development of adequate mathematical foundations for exact real computation. The seminar brought together researchers from many different disciplines who are working on theoretical or practical aspects of infinite computations. In this summary we describe the topics, the goals, and the contributions of the seminar.
Automata theory
computability in analysis
dataflow computation
hierarchies
infinite computations
infinite games
reactive systems
specification
1-5
Regular Paper
Peter
Hertling
Peter Hertling
Victor
Selivanov
Victor Selivanov
Wolfgang
Thomas
Wolfgang Thomas
William W.
Wadge
William W. Wadge
Klaus
Wagner
Klaus Wagner
10.4230/DagSemProc.08271.2
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Cartesian Programming: The TransLucid Programming Language
The TransLucid programming language is a low-level intensional language, designed to be sufficiently rich for it to be the target language for translating the common programming paradigms into it, while still being fully declarative. The objects manipulated by TransLucid, called hyperdatons, are arbitrary-dimensional infinite arrays, indexed by multidimensional tuples of arbitrary types. We present the syntax, denotational and operational semantics for a simple TransLucid system, consisting of 1) a header detailing how expressions should be parsed, 2) a set of libraries of types, and operations thereon, defined in a host language, 3) a set of TransLucid equations, and 4) a TransLucid demand to be evaluated. The evaluation of a demand for an (identifier, context) pair is undertaken using eduction, where previously computed pairs are stored in a cache called a warehouse. The execution ensures that only those dimensions actually encountered during the execution of an expression are taken into account when caching intermediate results.
Cartesian programming
Lucid language
declarative programming
multidimensional programming
context-aware programming
semantics.
1-16
Regular Paper
John
Plaice
John Plaice
Blanca
Mancilla
Blanca Mancilla
10.4230/DagSemProc.08271.3
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Declarative Synchronous Multithreaded Programming
We demonstrate how TransLucid can be used as a reactive system. At each instant, there is a set of active ports, where sets of equations, demands and threads are all registered. Each thread defines a sequence of (state, demand) pairs, and threads may interact through the overall set of equations. The entire system remains fully declarative.
Synchronous programming
distributed computing
declarative programming
Cartesian programming
multidimensional programming.
1-6
Regular Paper
Blanca
Mancilla
Blanca Mancilla
John
Plaice
John Plaice
10.4230/DagSemProc.08271.4
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General Logic Programs as Infinite Games
In [vE86] M.H. van Emden introduced a simple game semantics for definite logic programs. Recently [RW05,GRW05], the authors extended this game to apply to logic programs with negation. Moreover, under the assumption that the programs have a finite number of rules, it was demonstrated in [RW05,GRW05] that the game is equivalent to the well-founded semantics of negation. In this paper we present work-in-progress towards demonstrating that the game of [RW05,GRW05] is equivalent to the well-founded semantics even in the case of programs that have a countably infinite number of rules. We argue however that in this case the proof of correctness has to be more involved. More specifically, in order to demonstrate that the game is correct one has to define a refined game in which each of the two players in his first move makes a bet in the form of a countable ordinal. Each ordinal can be considered as a kind of clock that imposes a "time limit" to the moves of the corresponding player. We argue that this refined game can be used to give the proof of correctness for the countably infinite case.
Infinite Games
Negation in Logic Programming
Well-Founded Semantics
1-11
Regular Paper
Chrysida
Galanaki
Chrysida Galanaki
Panos
Rondogiannis
Panos Rondogiannis
William W.
Wadge
William W. Wadge
10.4230/DagSemProc.08271.5
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On the Semantic Approaches to Boolean Grammars
Boolean grammars extend context-free grammars by allowing conjunction and negation in rule bodies. This new formalism appears to be quite expressive and still efficient from a parsing point of view. Therefore, it seems reasonable to hope that boolean grammars can lead to more expressive tools that can facilitate the compilation process of modern programming languages. One important aspect concerning the theory of boolean grammars is their semantics. More specifically, the existence of negation makes it difficult to define a simple derivation-style semantics (such as for example in the case of context-free grammars). There have already been proposed a number of different semantic approaches in the literature. The purpose of this paper is to present the basic ideas behind each method and identify certain interesting problems that can be the object of further study in this area.
Boolean Grammars
Negation in Formal Grammars
Well-Founded Semantics
1-12
Regular Paper
Vassilis
Kountouriotis
Vassilis Kountouriotis
Christos
Nomikos
Christos Nomikos
Panos
Rondogiannis
Panos Rondogiannis
10.4230/DagSemProc.08271.6
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Topological Complexity of omega-Powers: Extended Abstract
The operation of taking the omega-power $V^omega$ of a language $V$ is a fundamental operation over finitary languages leading to omega-languages. Since the set $X^omega$ of infinite words over a finite alphabet $X$ can be equipped with the usual Cantor topology, the question of the topological complexity of omega-powers of finitary languages naturally arises and has been posed by Damian Niwinski (1990), Pierre Simonnet (1992), and Ludwig Staiger (1997). We investigate the topological complexity of omega-powers. We prove the following very surprising results which show that omega-powers exhibit a great opological complexity: for each non-null countable ordinal $xi$, there exist some $Sigma^0_xi$-complete omega-powers, and some $Pi^0_xi$-complete omega-powers. On the other hand, the Wadge hierarchy is a great refinement of the Borel hierarchy, determined by Bill Wadge. We show that, for each ordinal $xi$ greater than or equal to 3, there are uncountably many Wadge degrees of omega-powers of Borel rank $xi +1$. Using tools of effective descriptive set theory, we prove some effective versions of the above results.
Infinite words
omega-languages
omega-powers
Cantor topology
topological complexity
Borel sets
Borel ranks
complete sets
Wadge hierarchy
Wadge
1-9
Regular Paper
Olivier
Finkel
Olivier Finkel
Dominique
Lecomte
Dominique Lecomte
10.4230/DagSemProc.08271.7
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