Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science最新文献_第2页

Ground reducibility is EXPTIME-complete 地面还原性是EXPTIME-complete

Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science Pub Date : 1997-06-29 DOI: 10.1109/LICS.1997.614922

Hubert Comon-Lundh, Florent Jacquemard

{"title":"Ground reducibility is EXPTIME-complete","authors":"Hubert Comon-Lundh, Florent Jacquemard","doi":"10.1109/LICS.1997.614922","DOIUrl":"https://doi.org/10.1109/LICS.1997.614922","url":null,"abstract":"We prove that ground reducibility is EXPTIME-complete in the general case. EXPTIME-hardness is proved by encoding the computations of an alternating Turing machine whose space is polynomially bounded. It is more difficult to show that ground reducibility belongs to DEXPTIME. We associate first an automaton with disequality constraints A/sub R,t/ to a rewrite system R and a term t. This automaton is deterministic and accepts a term u if and only if t is not ground reducible by R. The number of states of A/sub R,t/ is O(2/sup /spl par/R/spl par//spl times//spl par/t/spl par//) and the size of the constraints are polynomial in the size of R,t. Then we prove some new pumping lemmas, using a total ordering on the computations of the automaton. Thanks to these lemmas, we can give an upper bound to the number of distinct subtrees of a minimal successful computation of an automaton with disequality constraints. It follows that emptiness of such an automaton can be decided in time polynomial in the number of its states and exponential in the size of its constraints. Altogether, we get a simply exponential deterministic algorithm for ground reducibility.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130521827","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}

引用次数: 62

Combination of compatible reduction orderings that are total on ground terms 兼容的减少订单的组合，总地面条件

Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science Pub Date : 1997-06-29 DOI: 10.1109/LICS.1997.614917

F. Baader

引用次数: 10

Complexity of two-variable logic with counting 带计数的二变量逻辑的复杂性

Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science Pub Date : 1997-06-29 DOI: 10.1109/LICS.1997.614958

L. Pacholski, W. Szwast, Lidia Tendera

引用次数: 88

Continuation models are universal for /spl lambda//sub /spl mu//-calculus 延拓模型是通用的/spl lambda//sub /spl mu//-微积分

Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science Pub Date : 1997-06-29 DOI: 10.1109/LICS.1997.614964

M. Hofmann, T. Streicher

引用次数: 15

Set constraints with intersection 设置有交集的约束

Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science Pub Date : 1997-06-29 DOI: 10.1109/LICS.1997.614962

Witold Charatonik, A. Podelski

引用次数: 40

On the forms of locality over finite models 有限模型的局部性形式

Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science Pub Date : 1997-06-29 DOI: 10.1109/LICS.1997.614948

L. Libkin

{"title":"On the forms of locality over finite models","authors":"L. Libkin","doi":"10.1109/LICS.1997.614948","DOIUrl":"https://doi.org/10.1109/LICS.1997.614948","url":null,"abstract":"Most proofs showing limitations of expressive power of first-order logic rely on Ehrenfeucht-Fraisse games. Playing the game often involves a nontrivial combinatorial argument, so it was proposed to find easier tools for proving expressivity bounds. Most of those known for first-order logic are based on its \"locality\", that is defined in different ways. In this paper we characterize the relationship between those notions of locality. We note that Gaifman's locality theorem gives rise to two notions: one deals with sentences and one with open formulae. We prove that the former implies Hauf's notion of locality, which in turn implies Gaifman's locality for open formulae. Each of these implies the bounded degree property, which is one of the easiest tools for proving expressivity bounds. These results apply beyond the first-order case. We use them to derive expressivity bounds for first-order logic with unary quantifiers and counting. Finally, we apply these results to relational database languages with aggregate functions, and prove that purely relational queries defined in such languages satisfy Gaifman's notion of locality. From this we derive a number of expressivity bounds for languages with aggregates.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132276377","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}

引用次数: 28

Semantics of exact real arithmetic 精确实算术的语义

Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science Pub Date : 1997-06-29 DOI: 10.1109/LICS.1997.614952

P. J. Potts, A. Edalat, M. Escardó

引用次数: 51

A logic for reasoning with higher-order abstract syntax 用高阶抽象语法进行推理的逻辑

Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science Pub Date : 1997-06-29 DOI: 10.1109/LICS.1997.614968

R. McDowell, D. Miller

{"title":"A logic for reasoning with higher-order abstract syntax","authors":"R. McDowell, D. Miller","doi":"10.1109/LICS.1997.614968","DOIUrl":"https://doi.org/10.1109/LICS.1997.614968","url":null,"abstract":"Logical frameworks based on intuitionistic or linear logics with higher-type quantification have been successfully used to give high-level, modular, and formal specifications of many important judgments in the area of programming languages and inference systems. Given such specifications, it is natural to consider proving properties about the specified systems in the framework: for example, given the specification of evaluation for a functional programming language, prove that the language is deterministic or that the subject-reduction theorem holds. One challenge in developing a framework for such reasoning is that higher-order abstract syntax (HOAS), an elegant and declarative treatment of object-level abstraction and substitution, is difficult to treat in proofs involving induction. In this paper we present a meta-logic that can be used to reason about judgments coded using HOAS; this meta-logic is an extension of a simple intuitionistic logic that admits higher-order quantification over simply typed /spl lambda/-terms (key ingredients for HOAS) as well as induction and a notion of definition. The latter concept of a definition is a proof-theoretic device that allows certain theories to be treated as \"closed\" or as defining fixed points. The resulting meta-logic can specify various logical frameworks and a large range of judgments regarding programming languages and inference systems. We illustrate this point through examples, including the admissibility of cut for a simple logic and subject reduction, determinacy of evaluation, and the equivalence of SOS and natural semantics presentations of evaluation for a simple functional programming language.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132261262","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}

引用次数: 67

Discrimination by parallel observers 平行观察员的歧视

Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science Pub Date : 1997-06-29 DOI: 10.1109/LICS.1997.614965

M. Dezani-Ciancaglini, J. Tiuryn, P. Urzyczyn

引用次数: 17

Two-variable logic with counting is decidable 带计数的双变量逻辑是可决定的

Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science Pub Date : 1997-06-29 DOI: 10.1109/LICS.1997.614957

E. Grädel, M. Otto, Eric Rosen

引用次数: 206