{"title":"Linear types and non-size-increasing polynomial time computation","authors":"M. Hofmann","doi":"10.1109/LICS.1999.782641","DOIUrl":"https://doi.org/10.1109/LICS.1999.782641","url":null,"abstract":"We propose a linear type system with recursion operators for inductive datatypes which ensures that all definable functions are polynomial time computable. The system improves upon previous such systems in that recursive definitions can be arbitrarily nested, in particular no predicativity or modality restrictions are made.","PeriodicalId":352531,"journal":{"name":"Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158)","volume":"2012 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128080962","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}
H. Devarajan, Dominic J. D. Hughes, G. Plotkin, V. Pratt
{"title":"Full completeness of the multiplicative linear logic of Chu spaces","authors":"H. Devarajan, Dominic J. D. Hughes, G. Plotkin, V. Pratt","doi":"10.1109/LICS.1999.782619","DOIUrl":"https://doi.org/10.1109/LICS.1999.782619","url":null,"abstract":"We prove full completeness of multiplicative linear logic (MLL) without MIX under the Chu interpretation. In particular we show that the cut-free proofs of MLL theorems are in a natural bijection with the binary logical transformations of the corresponding operations on the category of Chu spaces on a two-letter alphabet.","PeriodicalId":352531,"journal":{"name":"Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158)","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124571425","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":"Parikh's theorem in commutative Kleene algebra","authors":"M. Hopkins, D. Kozen","doi":"10.1109/LICS.1999.782634","DOIUrl":"https://doi.org/10.1109/LICS.1999.782634","url":null,"abstract":"Parikh's theorem says that, the commutative image of every context free language is the commutative image of some regular set. Pilling has shown that this theorem is essentially a statement about least solutions of polynomial inequalities. We prove the following general theorem of commutative Kleene algebra, of which Parikh's and Pilling's theorems are special cases: Every finite system of polynomial inequalities f/sub i/(x/sub 1/,...,x/sub n/)/spl les/x/sub i/, 1/spl les/i/spl les/n, over a commutative Kleene algebra K has a unique least solution in K/sup n/; moreover, the components of the solution are given by polynomials in the coefficients of the f/sub i/. We also give a closed-form solution in terms of the Jacobian matrix of the system.","PeriodicalId":352531,"journal":{"name":"Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128832766","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":"Subtyping recursive types in kernel Fun","authors":"Dario Colazzo, G. Ghelli","doi":"10.1109/LICS.1999.782605","DOIUrl":"https://doi.org/10.1109/LICS.1999.782605","url":null,"abstract":"The problem of defining and checking a subtype relation between recursive types was studied in Armadio and Cardelli (1993) for a first order type system, but for second order systems, which combine subtyping and parametric polymorphism, only negative results are known. This paper studies the problem of subtype checking for recursive types in system kernel Fun, a typed /spl lambda/-calculus with subtyping and bounded second order polymorphism. Along the lines of Armadio and Cardelli (1993), we study the definition of a subtype relation over kernel Fun recursive types, and then we present a subtyping algorithm which is sound and complete with respect to this relation. We show that the natural extension of the techniques introduced in Armadio and Cardelli (1993) to compare first order recursive types gives a non complete algorithm. We prove the completeness and correctness of a different algorithm, which also admits an efficient implementation.","PeriodicalId":352531,"journal":{"name":"Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116950018","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 bunched predicate logic","authors":"D. Pym","doi":"10.1109/LICS.1999.782614","DOIUrl":"https://doi.org/10.1109/LICS.1999.782614","url":null,"abstract":"We present the logic of bunched implications, BI, in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side. The propositional version of BI arises from an analysis of the proof-theoretic relationship between conjunction and implication, and may be viewed as a merging of intuitionistic logic and multiplicative, intuitionistic linear logic. The predicate version of BI includes, in addition to usual additive quantifiers, multiplicative (or intensional) quantifiers /spl forall//sub new/, and /spl exist//sub new/, which arise from observing restrictions on structural rules on the level of terms as well as propositions. Moreover, these restrictions naturally allow the distinction between additive predication and multiplicative predication for each propositional connective. We provide a natural deduction system, a sequent calculus, a Kripke semantics and a BHK semantics for BI. We mention computational interpretations, based on locality and sharing, at both the propositional and predicate levels. We explain BI's relationship with intuitionistic logic, linear logic and other relevant logics.","PeriodicalId":352531,"journal":{"name":"Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158)","volume":"20 13-14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123587973","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}
Miquel Bofill, Guillem Godoy, R. Nieuwenhuis, A. Rubio
{"title":"Paramodulation with non-monotonic orderings","authors":"Miquel Bofill, Guillem Godoy, R. Nieuwenhuis, A. Rubio","doi":"10.1109/LICS.1999.782618","DOIUrl":"https://doi.org/10.1109/LICS.1999.782618","url":null,"abstract":"All current completeness results for ordered paramodulation require the term ordering > to be well-founded, monotonic and total(izable) on ground terms. Here we introduce a new proof technique where the only properties required for > are well foundedness and the subterm property: The technique is a relatively simple and elegant application of some fundamental results on the termination and confluence of ground term rewrite systems (TRS). By a careful further analysis of our technique, we obtain the first Knuth-Bendix completion procedure that finds a convergent TRS for a given set of equations E and a (possibly non-totalizable) reduction ordering p whenever it exists. Note that being a reduction ordering is the minimal possible requirement on >, since a TRS terminates if, and only if, it is contained in a reduction ordering.","PeriodicalId":352531,"journal":{"name":"Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126307240","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 Hoare logic and Kleene algebra with tests","authors":"D. Kozen","doi":"10.1109/LICS.1999.782610","DOIUrl":"https://doi.org/10.1109/LICS.1999.782610","url":null,"abstract":"We show that Kleene algebra with tests subsumes propositional Hoare logic. Thus the specialized syntax and deductive apparatus of Hoare logic are inessential and can be replaced by simple equational reasoning. We show using this reduction that propositional Hoare logic is PSPACE-complete.","PeriodicalId":352531,"journal":{"name":"Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158)","volume":"168 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116351957","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":"Some decision problems of enormous complexity","authors":"H. Friedman","doi":"10.1109/LICS.1999.782577","DOIUrl":"https://doi.org/10.1109/LICS.1999.782577","url":null,"abstract":"We present some new decision and comparison problems of unusually high computational complexity. Most of the problems are strictly combinatorial in nature; others involve basic logical notions. Their complexities range from iterated exponential time completeness to /spl isin//sub 0/ time completeness to /spl theta/(/spl Omega//sup /spl omega//,0) time completeness to /spl theta/(/spl Omega//sub /spl omega//,0) time completeness. These three ordinals are well known ordinals from proof theory, and their associated complexity classes represent new levels of computational complexity for natural decision problems. Proofs will appear in an extended version of this manuscript to be published elsewhere.","PeriodicalId":352531,"journal":{"name":"Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158)","volume":"348 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132999776","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":"Reasoning about common knowledge with infinitely many agents","authors":"Joseph Y. Halpern, R. Shore","doi":"10.1109/LICS.1999.782633","DOIUrl":"https://doi.org/10.1109/LICS.1999.782633","url":null,"abstract":"Complete axiomatizations and exponential-time decision procedures are provided for reasoning about knowledge and common knowledge when there are infinitely many agents. The results show that reasoning about knowledge and common knowledge with infinitely many agents is no harder than when there are finitely many agents, provided that we can check the cardinality of certain set differences G G' where G and G' are sets of agents. Since our complexity results are independent of the cardinality of the sets G involved, they represent improvements over the previous results even with the sets of agents involved are finite. Moreover, our results make clear the extent to which issues of complexity and completeness depend on how the sets of agents involved are represented.","PeriodicalId":352531,"journal":{"name":"Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158)","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125084160","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":"Proving security protocols correct","authors":"Lawrence Charles Paulson","doi":"10.1109/LICS.1999.782632","DOIUrl":"https://doi.org/10.1109/LICS.1999.782632","url":null,"abstract":"Security protocols use cryptography to set up private communication channels on an insecure network. Many protocols contain flaws, and because security goals are seldom specified in detail, we cannot be certain what constitutes a flaw. Thanks to recent work by a number of researchers, security protocols can now be analyzed formally. The paper outlines the problem area, emphasizing the notion of freshness. It describes how a protocol can be specified using operational semantics and properties proved by rule induction, with machine support from the proof tool Isabelle. The main example compares two versions of the Yahalom protocol. Unless the model of the environment is sufficiently detailed, it cannot distinguish the correct protocol from a flawed version. The paper attempts to draw some general lessons on the use of formalisms. Compared with model checking, the inductive method performs a finer analysis, but the cost of using it is greater.","PeriodicalId":352531,"journal":{"name":"Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158)","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122984060","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}