Pub Date : 1992-06-22DOI: 10.1109/LICS.1992.185550
Nils Klarlund
Using the concept of a progress measure, a simplified proof is given of M.O. Rabin's (1969) fundamental result that the languages defined by tree automata are closed under complementation. To do this, it is shown that for infinite games based on tree automata, the forgetful determinacy property of Y. Gurevich and L. Harrington (1982) can be strengthened to an immediate determinacy property for the player who is trying to win according to a Rabin acceptance condition. Moreover, a graph-theoretic duality theorem for such acceptance conditions is shown. Also presented is a strengthened version of S. Safra's (1988) determinization construction. Together these results and the determinacy of Borel games yield a straightforward method for complementing tree automata.<>
{"title":"Progress measures, immediate determinacy, and a subset construction for tree automata","authors":"Nils Klarlund","doi":"10.1109/LICS.1992.185550","DOIUrl":"https://doi.org/10.1109/LICS.1992.185550","url":null,"abstract":"Using the concept of a progress measure, a simplified proof is given of M.O. Rabin's (1969) fundamental result that the languages defined by tree automata are closed under complementation. To do this, it is shown that for infinite games based on tree automata, the forgetful determinacy property of Y. Gurevich and L. Harrington (1982) can be strengthened to an immediate determinacy property for the player who is trying to win according to a Rabin acceptance condition. Moreover, a graph-theoretic duality theorem for such acceptance conditions is shown. Also presented is a strengthened version of S. Safra's (1988) determinization construction. Together these results and the determinacy of Borel games yield a straightforward method for complementing tree automata.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"95 1","pages":"382-393"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75184139","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 : 1992-06-22DOI: 10.1109/LICS.1992.185541
Anil Seth
The author shows a class of type-two feasible functionals, C/sub 2/, that satisfies Cook's conditions, (1990) and cannot be expressed as the lambda closure of type-one poly-time functions and any recursively enumerable set of type-two feasible functionals. Further, no class of total type-two functionals containing this class is representable as the lambda closure of a recursively enumerable set of type-two total computable functionals and type-one poly-time functions. The definition of C/sub 2/ provides a clear computational procedure for functionals of C/sub 2/. Using functionals of class C/sub 2/ a more general notion of polynomial-time reducibility between two arbitrary type-one functions can be introduced.<>
{"title":"There is no recursive axiomatization for feasible functionals of type 2","authors":"Anil Seth","doi":"10.1109/LICS.1992.185541","DOIUrl":"https://doi.org/10.1109/LICS.1992.185541","url":null,"abstract":"The author shows a class of type-two feasible functionals, C/sub 2/, that satisfies Cook's conditions, (1990) and cannot be expressed as the lambda closure of type-one poly-time functions and any recursively enumerable set of type-two feasible functionals. Further, no class of total type-two functionals containing this class is representable as the lambda closure of a recursively enumerable set of type-two total computable functionals and type-one poly-time functions. The definition of C/sub 2/ provides a clear computational procedure for functionals of C/sub 2/. Using functionals of class C/sub 2/ a more general notion of polynomial-time reducibility between two arbitrary type-one functions can be introduced.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"76 1","pages":"286-295"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79964918","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 : 1992-06-22DOI: 10.1109/LICS.1992.185536
P. Lincoln, John C. Mitchell
It is proved that the standard sequent calculus proof system of linear logic is equivalent to a natural deduction style proof system. The natural deduction system is used to investigate the pragmatic problems of type inference and type safety for a linear lambda calculus. Although terms do not have a single most-general type (for either the standard sequent presentation or the natural deduction formulation), there is a set of most-general types that may be computed using unification. The natural deduction system also facilitates the proof that the type of an expression is preserved by any evaluation step. An execution model and implementation is described, using a variant of the three-instruction machine. A novel feature of the implementation is that garbage-collected nonlinear memory is distinguished from linear memory, which does not require garbage collection and for which it is possible to do secure update in place.<>
{"title":"Operational aspects of linear lambda calculus","authors":"P. Lincoln, John C. Mitchell","doi":"10.1109/LICS.1992.185536","DOIUrl":"https://doi.org/10.1109/LICS.1992.185536","url":null,"abstract":"It is proved that the standard sequent calculus proof system of linear logic is equivalent to a natural deduction style proof system. The natural deduction system is used to investigate the pragmatic problems of type inference and type safety for a linear lambda calculus. Although terms do not have a single most-general type (for either the standard sequent presentation or the natural deduction formulation), there is a set of most-general types that may be computed using unification. The natural deduction system also facilitates the proof that the type of an expression is preserved by any evaluation step. An execution model and implementation is described, using a variant of the three-instruction machine. A novel feature of the implementation is that garbage-collected nonlinear memory is distinguished from linear memory, which does not require garbage collection and for which it is possible to do secure update in place.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"148 1","pages":"235-246"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83807397","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 : 1992-06-22DOI: 10.1109/LICS.1992.185519
E. Grädel, G. McColm
It is shown that transitive closure logic (FO+TC) is strictly more powerful than deterministic transitive closure logic (FO+DTC) on unordered structures. In fact, on certain classes of graphs, such as hypercubes or regular graphs of large degree and girth, every query in (FO+DTC) is first-order expressible. On the other hand, there are simple (FO+pos TC) queries on these classes that cannot be defined by first-order formulas.<>
{"title":"Deterministic vs. nondeterministic transitive closure logic","authors":"E. Grädel, G. McColm","doi":"10.1109/LICS.1992.185519","DOIUrl":"https://doi.org/10.1109/LICS.1992.185519","url":null,"abstract":"It is shown that transitive closure logic (FO+TC) is strictly more powerful than deterministic transitive closure logic (FO+DTC) on unordered structures. In fact, on certain classes of graphs, such as hypercubes or regular graphs of large degree and girth, every query in (FO+DTC) is first-order expressible. On the other hand, there are simple (FO+pos TC) queries on these classes that cannot be defined by first-order formulas.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"151 1","pages":"58-63"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86163716","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 : 1992-06-22DOI: 10.1109/LICS.1992.185522
Hiroshi Nakano
The catch/throw mechanism, a programming construct for nonlocal exit, plays an important role when programmers handle exceptional situations. A constructive formalization that captures the mechanism in the proofs-as-programs notion is given. A modified version of LJ equipped with inference rules corresponding to the operations of catch and throw is introduced. Then it is shown that one can actually extract programs that made use of the catch/throw mechanism from proofs under a certain realizability interpretation. Although the catch/throw mechanism provides only a restricted access to the current continuation, the formulation remains constructive.<>
{"title":"A constructive formalization of the catch and throw mechanism","authors":"Hiroshi Nakano","doi":"10.1109/LICS.1992.185522","DOIUrl":"https://doi.org/10.1109/LICS.1992.185522","url":null,"abstract":"The catch/throw mechanism, a programming construct for nonlocal exit, plays an important role when programmers handle exceptional situations. A constructive formalization that captures the mechanism in the proofs-as-programs notion is given. A modified version of LJ equipped with inference rules corresponding to the operations of catch and throw is introduced. Then it is shown that one can actually extract programs that made use of the catch/throw mechanism from proofs under a certain realizability interpretation. Although the catch/throw mechanism provides only a restricted access to the current continuation, the formulation remains constructive.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"16 1","pages":"82-89"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83441729","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 : 1992-06-22DOI: 10.1109/LICS.1992.185539
D. Caucal
The monadic second-order theory of term rewritings is considered. It is shown that the monadic theory of the rewriting (or the suffix rewriting) of a ground rewrite system is undecidable. Furthermore, the first-order theory is undecidable for the prefix derivation according to a linear context-free grammar on linear terms. Nevertheless, a new notion on terms with variables is introduced: a term is entire if each of its subterms either is a variable, or is without variable or has the same variables as the term. It is shown that the monadic theory is decidable (respectively undecidable) for the prefix rewriting according to a rewrite system on entire terms, with an axiom (respectively without axiom).<>
{"title":"Monadic theory of term rewritings","authors":"D. Caucal","doi":"10.1109/LICS.1992.185539","DOIUrl":"https://doi.org/10.1109/LICS.1992.185539","url":null,"abstract":"The monadic second-order theory of term rewritings is considered. It is shown that the monadic theory of the rewriting (or the suffix rewriting) of a ground rewrite system is undecidable. Furthermore, the first-order theory is undecidable for the prefix derivation according to a linear context-free grammar on linear terms. Nevertheless, a new notion on terms with variables is introduced: a term is entire if each of its subterms either is a variable, or is without variable or has the same variables as the term. It is shown that the monadic theory is decidable (respectively undecidable) for the prefix rewriting according to a rewrite system on entire terms, with an axiom (respectively without axiom).<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"11 1","pages":"266-273"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84220363","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 : 1992-06-22DOI: 10.1109/LICS.1992.185515
D. Kapur, P. Narendran
An algorithm for computing a complete set of unifiers for two terms involving associative-commutative function symbols is presented. It is based on a nondeterministic algorithm given by the authors in 1986 to show the NP-completeness of associative-commutative unifiability. The algorithm is easy to understand, and its termination can be easily established. Its complexity is easily analyzed and shown to be doubly exponential in the size of the input terms. The analysis also shows that there is a double-exponential upper bound on the size of a complete set of unifiers of two input terms. Since there is a family of simple associative-commutative unification problems which have complete sets of unifiers whose size is doubly exponential, the algorithm is optimal in its order of complexity in this sense.<>
{"title":"Double-exponential complexity of computing a complete set of AC-unifiers","authors":"D. Kapur, P. Narendran","doi":"10.1109/LICS.1992.185515","DOIUrl":"https://doi.org/10.1109/LICS.1992.185515","url":null,"abstract":"An algorithm for computing a complete set of unifiers for two terms involving associative-commutative function symbols is presented. It is based on a nondeterministic algorithm given by the authors in 1986 to show the NP-completeness of associative-commutative unifiability. The algorithm is easy to understand, and its termination can be easily established. Its complexity is easily analyzed and shown to be doubly exponential in the size of the input terms. The analysis also shows that there is a double-exponential upper bound on the size of a complete set of unifiers of two input terms. Since there is a family of simple associative-commutative unification problems which have complete sets of unifiers whose size is doubly exponential, the algorithm is optimal in its order of complexity in this sense.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"49 1","pages":"11-21"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74314547","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 : 1992-06-22DOI: 10.1109/LICS.1992.185524
D. Sangiorgi
The use of lambda calculus in richer settings, possibly involving parallelism, is examined in terms of its effect on the equivalence between lambda terms, focusing on S. Abramsky's (Ph.D thesis, Univ. of London, 1987) lazy lambda calculus. First, the lambda calculus is studied within a process calculus by examining the equivalence induced by R. Milner's (1992) encoding into the pi -calculus. Exact operational and denotational characterizations for this equivalence are given. Second, Abramsky's applicative bisimulation is examined when the lambda calculus is augmented with (well-formed) operators, i.e. symbols equipped with reduction rules describing their behavior. Then, maximal discrimination is obtained when all operators are considered; it is shown that this discrimination coincides with the one given by the above equivalence and that the adoption of certain nondeterministic operators is sufficient and necessary to induce it.<>
{"title":"The lazy lambda calculus in a concurrency scenario","authors":"D. Sangiorgi","doi":"10.1109/LICS.1992.185524","DOIUrl":"https://doi.org/10.1109/LICS.1992.185524","url":null,"abstract":"The use of lambda calculus in richer settings, possibly involving parallelism, is examined in terms of its effect on the equivalence between lambda terms, focusing on S. Abramsky's (Ph.D thesis, Univ. of London, 1987) lazy lambda calculus. First, the lambda calculus is studied within a process calculus by examining the equivalence induced by R. Milner's (1992) encoding into the pi -calculus. Exact operational and denotational characterizations for this equivalence are given. Second, Abramsky's applicative bisimulation is examined when the lambda calculus is augmented with (well-formed) operators, i.e. symbols equipped with reduction rules describing their behavior. Then, maximal discrimination is obtained when all operators are considered; it is shown that this discrimination coincides with the one given by the above equivalence and that the adoption of certain nondeterministic operators is sufficient and necessary to induce it.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"22 1","pages":"102-109"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87043733","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 : 1992-06-22DOI: 10.1109/LICS.1992.185557
Ugo de'Liguoro, A. Piperno, R. Statman
Retractions existing in all models of simply typed lambda -calculus are studied and related to other relations among types, such as isomorphisms, surjections, and injections. A formal system to deduce the existence of such retractions is shown to be sound and complete with respect to retractions definable by linear lambda -terms. Results aiming at a system complete with respect to the provable retractions tout court are established.<>
{"title":"Retracts in simply type lambda beta eta -calculus","authors":"Ugo de'Liguoro, A. Piperno, R. Statman","doi":"10.1109/LICS.1992.185557","DOIUrl":"https://doi.org/10.1109/LICS.1992.185557","url":null,"abstract":"Retractions existing in all models of simply typed lambda -calculus are studied and related to other relations among types, such as isomorphisms, surjections, and injections. A formal system to deduce the existence of such retractions is shown to be sound and complete with respect to retractions definable by linear lambda -terms. Results aiming at a system complete with respect to the provable retractions tout court are established.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"59 1","pages":"461-469"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90628188","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 : 1992-06-22DOI: 10.1109/LICS.1992.185533
M. Kanovich
The question of developing a computational interpretation of J.-Y. Girard's (1987) linear logic and obtaining efficient decision algorithms for this logic, based on the bottom-up approach, is addressed. The approach taken is to start with the simplest natural fragment of linear logic and then expand it step-by-step. The smallest natural Horn fragment of Girard's linear logic is considered, and it is proved that this fragment is NP-complete. As a corollary, an affirmative solution for the problem of whether the multiplicative fragment of Girard's linear logic is NP-complete is obtained. Then a complete computational interpretation for Horn fragments enriched by two additive connectives and by the storage operator is given. Within the framework of this interpretation, it becomes possible to explicitly formalize and clarify the computational aspects of the fragments of linear logic in question and establish exactly the complexity level of these fragments.<>
{"title":"Horn programming in linear logic is NP-complete","authors":"M. Kanovich","doi":"10.1109/LICS.1992.185533","DOIUrl":"https://doi.org/10.1109/LICS.1992.185533","url":null,"abstract":"The question of developing a computational interpretation of J.-Y. Girard's (1987) linear logic and obtaining efficient decision algorithms for this logic, based on the bottom-up approach, is addressed. The approach taken is to start with the simplest natural fragment of linear logic and then expand it step-by-step. The smallest natural Horn fragment of Girard's linear logic is considered, and it is proved that this fragment is NP-complete. As a corollary, an affirmative solution for the problem of whether the multiplicative fragment of Girard's linear logic is NP-complete is obtained. Then a complete computational interpretation for Horn fragments enriched by two additive connectives and by the storage operator is given. Within the framework of this interpretation, it becomes possible to explicitly formalize and clarify the computational aspects of the fragments of linear logic in question and establish exactly the complexity level of these fragments.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"200-210"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83545240","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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