19th Annual Symposium on Foundations of Computer Science (sfcs 1978)最新文献

{"title":"The complexity of checkers on an N × N board","authors":"A. Fraenkel, M. Garey, David S. Johnson, T. Schaefer, Y. Yesha","doi":"10.1109/SFCS.1978.36","DOIUrl":"https://doi.org/10.1109/SFCS.1978.36","url":null,"abstract":"We consider the game of Checkers generalized to an N × N board. Although certain properties of positions are efficiently computable (e.g., can Black jump all of White's pieces in a single move?), the general question, given a position, of whether a specified player can force a win against best play by his opponent, is shown to be PSPACE-hard. Under certain reasonable assumptions about the \"drawing rule\" in force, the problem is itself in PSPACE and hence is PSPACE-complete.","PeriodicalId":346837,"journal":{"name":"19th Annual Symposium on Foundations of Computer Science (sfcs 1978)","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1978-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132420526","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":"A decidability result for a second order process logic","authors":"R. Parikh","doi":"10.1109/SFCS.1978.2","DOIUrl":"https://doi.org/10.1109/SFCS.1978.2","url":null,"abstract":"We prove the decidability of the validity problem for a rather general language for talking about computations. As corollaries of our result, we obtain some decidability results of Pratt, Constable, Fischer-Ladner, and Pnueli and also a new decidability result for deterministic propositional dynamic logic.","PeriodicalId":346837,"journal":{"name":"19th Annual Symposium on Foundations of Computer Science (sfcs 1978)","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1978-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133258171","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":"Model theoretic aspects of computational complexity","authors":"R. Lipton","doi":"10.1109/SFCS.1978.23","DOIUrl":"https://doi.org/10.1109/SFCS.1978.23","url":null,"abstract":"","PeriodicalId":346837,"journal":{"name":"19th Annual Symposium on Foundations of Computer Science (sfcs 1978)","volume":"171 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1978-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114338452","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":"Strassen's algorithm is not optimal trilinear technique of aggregating, uniting and canceling for constructing fast algorithms for matrix operations","authors":"V. Pan","doi":"10.1109/SFCS.1978.34","DOIUrl":"https://doi.org/10.1109/SFCS.1978.34","url":null,"abstract":"A new technique of trilinear operations of aggregating, uniting and canceling is introduced and applied to constructing fast linear non-commutative algorithms for matrix multiplication. The result is an asymptotic improvement of Strassen's famous algorithms for matrix operations.","PeriodicalId":346837,"journal":{"name":"19th Annual Symposium on Foundations of Computer Science (sfcs 1978)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1978-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114560153","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 average-case complexity of selecting k-th best","authors":"A. Yao, F. Yao","doi":"10.1109/SFCS.1978.29","DOIUrl":"https://doi.org/10.1109/SFCS.1978.29","url":null,"abstract":"Let Vk (n) be the minimum average number of pairwise comparisons needed to find the k-th largest of n numbers (k≥2), assuming that all n! orderings are equally likely. D. W. Matula proved that, for some absolute constant c, Vk(n)- n ≤ ck log log n as n → ∞. In the present paper, we show that there exists an absolute constant c′ ≫ 0 such that Vk(n) - n ≥ c′k log log n as n → ∞, proving a conjecture by Matula.","PeriodicalId":346837,"journal":{"name":"19th Annual Symposium on Foundations of Computer Science (sfcs 1978)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1978-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133639365","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":"Equality languages, fixed point languages and representations of recursively enumerable languages","authors":"J. Engelfriet, G. Rozenberg","doi":"10.1109/SFCS.1978.14","DOIUrl":"https://doi.org/10.1109/SFCS.1978.14","url":null,"abstract":"A considerable part of formal language'theory deals with mappings on free monoids. A way to measure the similarity of mappings a,a on the free monoid r* generated by an alphabet E is to consider the equality language of a and a denoted by Eq(a,8) and consisting of all words x in E* such that a(x) = 6(x). To measure the similarity of a mapping with the identity mapping on the same domain one considers the fixed point language of a de~oted by Fp(a) and consisting of all words x in E such that a(x) = x (if a is a relation in r* x E* then we take Fp(a) = {x £ E* : x £ a(x)}). Thus equality languages and fixed point languages are very natural from the mathematical point of view. If we consider homomorphisms of free monoids then their equality languages represent sets of instances of the Post correspondence Problem; in this sense considering equality languages of homomorphisms is a classical topic in formal language theory (and computability theory). A revival of interest in those languages was stimulated recently by research concerning some very challenging decision problems in formal language theory; it became apparent that in several cases equality languages of homomorphisms playa vital role in (positive!) solutions of some basic equivalence problems of L systems (see e.g. (2) and [4]). This paper is an attempt towards a systematic investigation of equality languages and fixed point languages of homomorphisms and dgsm mappings (i.e. mappings defined by deterministic generalized sequential machines with accepting states). Homomorphisms and dgsm mappings are certainly among the most important mappings in formal language theory and so they form a good departure point for building up a systematic theory. Related work appears in [3] and [8]. In this extended abstract we summarize\" some of the results we have obtained in this direction. It is organized as follows. Section 2 provides basic language-theoretic properties of equality languages and fixed point languages of homomorphisms. In Section 3 we present some results on the equality languages and fixed point languages of dgsm mappings but we concentrate on the subclass of dgsm mappings (that we introduce) called symmetric dgsm mappings. The theorem on fixed point languages of these mappings seems to be quite central in our theory. Then Section 4 provides an illustration of the usefulness of the classes of languages we have considered to provide various","PeriodicalId":346837,"journal":{"name":"19th Annual Symposium on Foundations of Computer Science (sfcs 1978)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1978-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125664573","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 recursive equations having a unique solution","authors":"B. Courcelle","doi":"10.1109/SFCS.1978.26","DOIUrl":"https://doi.org/10.1109/SFCS.1978.26","url":null,"abstract":"We give conditions on a left-linear Church-Rosser term rewriting system S allowing to define S-normal forms for infinite terms. We obtain a characterization of the S-equivalence of recursive program schemes (i.e. equivalence in all interpretations which validate S considered as a set of axioms). We give sufficient conditions for a recursive program scheme Σ to be S-univocal i.e. to have only one solution up to S-equivalence (considering Σ as a system of equations). For such schemes, we obtain proofs of S-equivalence which do not use any \"induction principle\". We also consider (SUE)-equivalence where S satisfies the above conditions and E is a set of bilinear equations such that no E-normal form does exist.","PeriodicalId":346837,"journal":{"name":"19th Annual Symposium on Foundations of Computer Science (sfcs 1978)","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1978-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129738049","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 algebra of order extended abstract","authors":"D. Lehmann","doi":"10.1109/SFCS.1978.28","DOIUrl":"https://doi.org/10.1109/SFCS.1978.28","url":null,"abstract":"Algebras whose carriers are partially ordered sets and operations are monotone and algebras whose carriers are complete partial orders and operations are continuous are studied. A quotient construction is provided for both types of algebras. The notion of a variety of algebras is defined and it is shown that the analogue of Birkhoff variety theorem holds for ordered algebras but not for continuous algebras. The results presented are a good first step towards a theory of ordered data types and a study of families of interpretations of schemas.","PeriodicalId":346837,"journal":{"name":"19th Annual Symposium on Foundations of Computer Science (sfcs 1978)","volume":"323 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1978-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129215019","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":"Data types as initial algebras: A unification of Scottery and ADJery","authors":"A. Kanda","doi":"10.1109/SFCS.1978.12","DOIUrl":"https://doi.org/10.1109/SFCS.1978.12","url":null,"abstract":"This paper presents a formulation within the framework of data types as initial algebras, of parameterizations of data types. We will observe that Scott's data type constructors like +, ×, and circular definitions are parameterizations in our sense. Thence we will provide a uniform ground to compare ADJ-like data types with Lehmann-Smyth's data types, and will justify recent ADJ's claim that polynomial data types of Lehmann-Smyth could be simulated within ADJery.","PeriodicalId":346837,"journal":{"name":"19th Annual Symposium on Foundations of Computer Science (sfcs 1978)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1978-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127832519","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":"Improving the bounds on optimal merging","authors":"C. Christen","doi":"10.1109/SFCS.1978.20","DOIUrl":"https://doi.org/10.1109/SFCS.1978.20","url":null,"abstract":"This paper presents a new merging algorithm and uses a counterstrategy argument to derive new upper and lower bounds on the complexity of the optimal merging problem. These improved bounds differ by at most ⌈ m/4 ⌉ comparisons, where m is the number of elements of the shorter sequence.","PeriodicalId":346837,"journal":{"name":"19th Annual Symposium on Foundations of Computer Science (sfcs 1978)","volume":"137 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1978-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127151882","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}