Pub Date : 2007-09-01DOI: 10.1142/9789812770998_0001
G. Ausiello
{"title":"Clairvoyance and Laziness for on Line Travelling Agents","authors":"G. Ausiello","doi":"10.1142/9789812770998_0001","DOIUrl":"https://doi.org/10.1142/9789812770998_0001","url":null,"abstract":"","PeriodicalId":212849,"journal":{"name":"Italian Conference on Theoretical Computer Science","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129230368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-09-01DOI: 10.1142/9789812770998_0017
Mathias Hauptmann
A polyomial time approximation scheme for an optimization problem X is an algorithm A such that for each instance x of X and each ǫ > 0, A computes a (1 + ǫ)-approximate solution to instance x of X in time is O(|x|f(1/ǫ)) for some function f . If the running time of A is instead bounded by g(1/ǫ) · |x|O(1) for some function g, A is called an efficient polynomial time approximation scheme. PTAS denotes the class of all NP optimization problems for which a polytime approximation scheme exists, and EPTAS is the class of all such problems for which an efficient polytime approximation scheme exists. It is an open question whether P 6= NP implies the strictness of the inclusion EPTAS ⊆ PTAS. Bazgan [2] and independently Cesati and Trevisan [5] gave a separation under the stronger assumption FPT 6= W [P ]. In this paper we prove EPTAS ( PTAS under some different assumption, namely existence of NP search problems ΠR with a superpolynomial lower bound for the deterministic time complexity. This assumption is weaker than the NP Machine Hypothesis [15] and hence is implied by the Measure Hypothesis μp(NP ) 6= 0. Furthermore, using a sophisticated combinatorial counting argument we construct a recursive oracle under which our assumption holds but that of Cesati and Trevisan does not hold, implying that using relativizing proof techniques one cannot show that our assumption implies FPT 6= W [P ].
优化问题X的多项式时间近似格式是这样一种算法A:对于X的每一个实例X，每一个O > 0, A计算一个(1 + O)——对于某个函数f，实例X (X)在时间上的近似解为O(| X |f(1/ O))。如果对于某个函数g, A的运行时间以g(1/ O)·|x|O(1)为界，则A被称为有效的多项式时间近似方案。PTAS表示存在多时近似方案的所有NP优化问题的类别，EPTAS表示存在有效多时近似方案的所有NP优化问题的类别。p6 = NP是否意味着包含EPTAS的严格性，这是一个有待解决的问题。Bazgan[2]和独立的Cesati和Trevisan[5]在更强的假设FPT 6= W [P]下给出了分离。本文在一些不同的假设下证明了EPTAS (PTAS)，即存在具有确定性时间复杂度的超多项式下界的NP搜索问题ΠR。该假设弱于NP机假设[15]，因此由度量假设μp(NP) 6= 0隐含。此外，使用一个复杂的组合计数论证，我们构造了一个递归预言，在这个预言下，我们的假设成立，而Cesati和Trevisan的假设不成立，这意味着使用相对证明技术，我们不能证明我们的假设意味着FPT 6= W [P]。
{"title":"The Measure Hypothesis and Efficiency of Polynomial Time Approximation Schemes","authors":"Mathias Hauptmann","doi":"10.1142/9789812770998_0017","DOIUrl":"https://doi.org/10.1142/9789812770998_0017","url":null,"abstract":"A polyomial time approximation scheme for an optimization problem X is an algorithm A such that for each instance x of X and each ǫ > 0, A computes a (1 + ǫ)-approximate solution to instance x of X in time is O(|x|f(1/ǫ)) for some function f . If the running time of A is instead bounded by g(1/ǫ) · |x|O(1) for some function g, A is called an efficient polynomial time approximation scheme. PTAS denotes the class of all NP optimization problems for which a polytime approximation scheme exists, and EPTAS is the class of all such problems for which an efficient polytime approximation scheme exists. It is an open question whether P 6= NP implies the strictness of the inclusion EPTAS ⊆ PTAS. Bazgan [2] and independently Cesati and Trevisan [5] gave a separation under the stronger assumption FPT 6= W [P ]. In this paper we prove EPTAS ( PTAS under some different assumption, namely existence of NP search problems ΠR with a superpolynomial lower bound for the deterministic time complexity. This assumption is weaker than the NP Machine Hypothesis [15] and hence is implied by the Measure Hypothesis μp(NP ) 6= 0. Furthermore, using a sophisticated combinatorial counting argument we construct a recursive oracle under which our assumption holds but that of Cesati and Trevisan does not hold, implying that using relativizing proof techniques one cannot show that our assumption implies FPT 6= W [P ].","PeriodicalId":212849,"journal":{"name":"Italian Conference on Theoretical Computer Science","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121313704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-09-01DOI: 10.1142/9789812770998_0005
G. Longo
Our mathematical relation to space originated by the symmetries at the core of Greek geometry as well as Riemann’s manifolds. Symmetries continued to provide the conceptual tools for further constructions of mathematical structures, from Poincare’s Geometry of Dynamical Systems to Category Theory, but were disregarded in logical foundations as Arithmetic has been considered, since Frege, the (only or paradigmatic) locus for foundational analyses. They are back now also in Logic, but a direct link to their role in Physics is still missing. As a matter of fact, geodetic principles, in Physics, originate in symmetries and provide an effective foundational frame for the main theoretical approaches, since the work by E. Noether and H. Weyl. The common “construction principles”, largely grounded on symmetries, may renew the foundational links between these two disciplines. Can computability fit into this renewed frame? What can it tell us about physical dynamics?
{"title":"Symmetries in Foundations","authors":"G. Longo","doi":"10.1142/9789812770998_0005","DOIUrl":"https://doi.org/10.1142/9789812770998_0005","url":null,"abstract":"Our mathematical relation to space originated by the symmetries at the core of Greek geometry as well as Riemann’s manifolds. Symmetries continued to provide the conceptual tools for further constructions of mathematical structures, from Poincare’s Geometry of Dynamical Systems to Category Theory, but were disregarded in logical foundations as Arithmetic has been considered, since Frege, the (only or paradigmatic) locus for foundational analyses. They are back now also in Logic, but a direct link to their role in Physics is still missing. As a matter of fact, geodetic principles, in Physics, originate in symmetries and provide an effective foundational frame for the main theoretical approaches, since the work by E. Noether and H. Weyl. The common “construction principles”, largely grounded on symmetries, may renew the foundational links between these two disciplines. Can computability fit into this renewed frame? What can it tell us about physical dynamics?","PeriodicalId":212849,"journal":{"name":"Italian Conference on Theoretical Computer Science","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127769515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-09-01DOI: 10.1142/9789812770998_0008
M. Bernardo, A. Aldini
Markovian process calculi constitute a useful framework for reasoning about the functional and performance aspects of concurrent systems. This is achieved by means of behavioral equivalences that take into account both the action names and their exponentially distributed durations. A notable extension to the expressiveness of Markovian process calculi derives from the adoption of GSPNlike immediate actions, i.e. actions with a zero duration and equipped with a priority level and a weight. Since internal immediate actions are unobservable both from the functional viewpoint and from the performance viewpoint, in this paper we tackle the problem of defining a weak variant of Markovian bisimilarity that abstracts from such actions. We show that the proposed equivalence is a congruence and admits a sound and complete axiomatization for the class of well-prioritized process terms.
{"title":"Weak Markovian Bisimilarity: Abstracting from Prioritized/Weighted Internal Immediate Actions","authors":"M. Bernardo, A. Aldini","doi":"10.1142/9789812770998_0008","DOIUrl":"https://doi.org/10.1142/9789812770998_0008","url":null,"abstract":"Markovian process calculi constitute a useful framework for reasoning about the functional and performance aspects of concurrent systems. This is achieved by means of behavioral equivalences that take into account both the action names and their exponentially distributed durations. A notable extension to the expressiveness of Markovian process calculi derives from the adoption of GSPNlike immediate actions, i.e. actions with a zero duration and equipped with a priority level and a weight. Since internal immediate actions are unobservable both from the functional viewpoint and from the performance viewpoint, in this paper we tackle the problem of defining a weak variant of Markovian bisimilarity that abstracts from such actions. We show that the proposed equivalence is a congruence and admits a sound and complete axiomatization for the class of well-prioritized process terms.","PeriodicalId":212849,"journal":{"name":"Italian Conference on Theoretical Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130673227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-09-01DOI: 10.1142/9789812770998_0006
Mathias Hauptmann
{"title":"On the Approximability of Dense Steiner Tree Problems","authors":"Mathias Hauptmann","doi":"10.1142/9789812770998_0006","DOIUrl":"https://doi.org/10.1142/9789812770998_0006","url":null,"abstract":"","PeriodicalId":212849,"journal":{"name":"Italian Conference on Theoretical Computer Science","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127069038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-09-01DOI: 10.1142/9789812770998_0020
G. D. Crescenzo, Ivan Visconti
One contribution provided by the groundbreaking concept of interactive proofs is the notion of proofs of knowledge, where a prover can convince a verifier that she knows a secret related to a public statement. This notion was formalized in the conventional complexity-theoretic model of interactive protocols and showed to be very useful for cryptographic applications, such as entity authentication schemes. Motivated by these applicability considerations, in this paper, we consider proofs of knowledge in a cryptographic model, called the bare public-key model (BPK model in short), where round-efficient interactive proofs with strong variants of security against provers (i.e., soundness) and security against verifiers (i.e., zero-knowledge) have been presented. We formally define notions of proofs of knowledge in the BPK model, and show that there are 4 distinct such notions for each of the previously studied four known notions of soundness. Finally, under the existence of any homomorphic one-way function family, (a generalization of) a 4-round argument system for all NP languages from the literature is a proof of knowledge that is secure against concurrent attacks from provers or verifiers.
{"title":"On Defining Proofs of Knowledge in the Bare Public Key Model","authors":"G. D. Crescenzo, Ivan Visconti","doi":"10.1142/9789812770998_0020","DOIUrl":"https://doi.org/10.1142/9789812770998_0020","url":null,"abstract":"One contribution provided by the groundbreaking concept of interactive proofs is the notion of proofs of knowledge, where a prover can convince a verifier that she knows a secret related to a public statement. This notion was formalized in the conventional complexity-theoretic model of interactive protocols and showed to be very useful for cryptographic applications, such as entity authentication schemes. Motivated by these applicability considerations, in this paper, we consider proofs of knowledge in a cryptographic model, called the bare public-key model (BPK model in short), where round-efficient interactive proofs with strong variants of security against provers (i.e., soundness) and security against verifiers (i.e., zero-knowledge) have been presented. We formally define notions of proofs of knowledge in the BPK model, and show that there are 4 distinct such notions for each of the previously studied four known notions of soundness. Finally, under the existence of any homomorphic one-way function family, (a generalization of) a 4-round argument system for all NP languages from the literature is a proof of knowledge that is secure against concurrent attacks from provers or verifiers.","PeriodicalId":212849,"journal":{"name":"Italian Conference on Theoretical Computer Science","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126557166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2007-09-01DOI: 10.1142/9789812770998_0002
H. Barendregt
The present invention relates to agrochemical agents of products based on azulmic acids stabilized by reaction with aminoplast-forming agents and carbonyl compounds or condensation products thereof.
本发明涉及一种农用化学剂，其产品基于与氨基质体形成剂和羰基化合物或其缩合产物反应稳定的唑酸。
{"title":"Proving the Range Property for Lambda Theories and Models","authors":"H. Barendregt","doi":"10.1142/9789812770998_0002","DOIUrl":"https://doi.org/10.1142/9789812770998_0002","url":null,"abstract":"The present invention relates to agrochemical agents of products based on azulmic acids stabilized by reaction with aminoplast-forming agents and carbonyl compounds or condensation products thereof.","PeriodicalId":212849,"journal":{"name":"Italian Conference on Theoretical Computer Science","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2007-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126731514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Two Variables Are Not Enough","authors":"R. Statman","doi":"10.1007/11560586_32","DOIUrl":"https://doi.org/10.1007/11560586_32","url":null,"abstract":"","PeriodicalId":212849,"journal":{"name":"Italian Conference on Theoretical Computer Science","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116860394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Computational Complexity of the L(2, 1)-Labeling Problem for Regular Graphs","authors":"J. Fiala, Jan Kratochvíl","doi":"10.1007/11560586_19","DOIUrl":"https://doi.org/10.1007/11560586_19","url":null,"abstract":"","PeriodicalId":212849,"journal":{"name":"Italian Conference on Theoretical Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130644188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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