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Giovanni Guida - One of the best experts on this subject based on the ideXlab platform.
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scc Recursiveness a general schema for argumentation semantics
Artificial Intelligence, 2005Co-Authors: Pietro Baroni, Massimiliano Giacomin, Giovanni GuidaAbstract:In argumentation theory, Dung's abstract framework provides a unifying view of several alternative semantics based on the notion of extension. In this context, we propose a general recursive schema for argumentation semantics, based on decomposition along the strongly connected components of the argumentation framework. We introduce the fundamental notion of SCC-Recursiveness and we show that all Dung's admissibility-based semantics are SCC-recursive, and therefore a special case of our schema. On these grounds, we argue that the concept of SCC-Recursiveness plays a fundamental role in the study and definition of argumentation semantics. In particular, the space of SCC-recursive semantics provides an ideal basis for the investigation of new proposals: starting from the analysis of several examples where Dung's preferred semantics gives rise to questionable results, we introduce four novel SCC-recursive semantics, able to overcome the limitations of preferred semantics, while differing in other respects.
Zakaria Bouziane - One of the best experts on this subject based on the ideXlab platform.
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a primitive recursive algorithm for the general petri net reachability problem
Foundations of Computer Science, 1998Co-Authors: Zakaria BouzianeAbstract:E. Mayr and R. Kosaraju (1981) proved the decidability of the general Petri net reachability problem. However their algorithms are non primitive recursive. Since then the primitive Recursiveness of this problem was stated as an open problem. In this paper we give a double exponential space algorithm for the general Petri net reachability problem.
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FOCS - A primitive recursive algorithm for the general Petri net reachability problem
Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280), 1Co-Authors: Zakaria BouzianeAbstract:E. Mayr and R. Kosaraju (1981) proved the decidability of the general Petri net reachability problem. However their algorithms are non primitive recursive. Since then the primitive Recursiveness of this problem was stated as an open problem. In this paper we give a double exponential space algorithm for the general Petri net reachability problem.
Svetlana Selivanova - One of the best experts on this subject based on the ideXlab platform.
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primitive recursive ordered fields and some applications
arXiv: Computational Complexity, 2020Co-Authors: Victor L Selivanov, Svetlana SelivanovaAbstract:We establish primitive recursive versions of some known facts about computable ordered fields of reals and computable reals, and then apply them to proving primitive Recursiveness of some natural problems in linear algebra and analysis. In particular, we find a partial primitive recursive analogue of Ershov-Madison's theorem about real closures of computable ordered fields, relate the corresponding fields to the primitive recursive reals, give sufficient conditions for primitive recursive root-finding, computing normal forms of matrices, and computing solution operators of some linear systems of PDE.
Pietro Baroni - One of the best experts on this subject based on the ideXlab platform.
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scc Recursiveness a general schema for argumentation semantics
Artificial Intelligence, 2005Co-Authors: Pietro Baroni, Massimiliano Giacomin, Giovanni GuidaAbstract:In argumentation theory, Dung's abstract framework provides a unifying view of several alternative semantics based on the notion of extension. In this context, we propose a general recursive schema for argumentation semantics, based on decomposition along the strongly connected components of the argumentation framework. We introduce the fundamental notion of SCC-Recursiveness and we show that all Dung's admissibility-based semantics are SCC-recursive, and therefore a special case of our schema. On these grounds, we argue that the concept of SCC-Recursiveness plays a fundamental role in the study and definition of argumentation semantics. In particular, the space of SCC-recursive semantics provides an ideal basis for the investigation of new proposals: starting from the analysis of several examples where Dung's preferred semantics gives rise to questionable results, we introduce four novel SCC-recursive semantics, able to overcome the limitations of preferred semantics, while differing in other respects.
Francesc Rossello - One of the best experts on this subject based on the ideXlab platform.
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Recursiveness over the complex numbers is time bounded
Foundations of Software Technology and Theoretical Computer Science, 1993Co-Authors: Felipe Cucker, Francesc RosselloAbstract:In their 1989 paper [2], L. Blum, M. Shub and S. Smale introduced a model of computation and a theory of Recursiveness that accepted an ordered field or ring as alphabet for the space of admissible inputs. A special emphasis was made in the ordered field of the real numbers, ~ . That work also made an a t tempt , under the structural approach to complexity, at a classification of the procedures developed in numerical analysis and computational geometry involving real numbers as inputs. In particular, analogues of the P and NP classes were introduced there. At first glance many similarities can be seen between the new complexity classes over the reals, with their relationships, and their Boolean counterparts, a very remarkable one being the existence of complete problems in the real analogues of NP ([2]) and P ([3]). However, many basic differences can also be found. An outstanding one is given by the fact that there are recursive problems without running time bounds for any machine solving them. A typical example is given by 7/ C ~ , a recursive set that cannot be decided in constant time and therefore, since all inputs have size 1, whithin any function bound on this input size. A characterization of subsets of B ~ that can be decided in bounded time as well as many properties concerning this class of sets can be found in [4]. Other example of computation where "recursive" does not coincide with "time bounded" are the integers with the algebraic cost; for details see [5]. In spite of the interest devoted to the field of the real numbers in [2], the theory of computation introduced there applies for any commutative ring, and the authors ask in section 11 of their paper "to explore an analogous theory for unordered fields such as C". First results about NP-complete problems over the complex numbers appear in [8]. The aim of this note is to show that over the complex numbers the situation regarding time bounded recursive sets turns out to be the Boolean one, i.e.
