We show that probabilistic computable functions, i.e., those functions outputting distributions and computed by probabilistic Turing machines, can be characterized by a natural generalization of Church and Kleene’s partial recursive functions. The obtained algebra, following Leivant, can be restricted so as to capture the notion of polytime sampleable distributions, a key concept in average-case complexity and cryptography.
{"title":"Probabilistic Recursion Theory and Implicit Computational Complexity","authors":"Ugo Dal Lago, Sara Zuppiroli, M. Gabbrielli","doi":"10.7561/SACS.2014.2.177","DOIUrl":"https://doi.org/10.7561/SACS.2014.2.177","url":null,"abstract":"We show that probabilistic computable functions, i.e., those functions outputting distributions and computed by probabilistic Turing machines, can be characterized by a natural generalization of Church and Kleene’s partial recursive functions. The obtained algebra, following Leivant, can be restricted so as to capture the notion of polytime sampleable distributions, a key concept in average-case complexity and cryptography.","PeriodicalId":53862,"journal":{"name":"Scientific Annals of Computer Science","volume":"1 1","pages":"97-114"},"PeriodicalIF":0.9,"publicationDate":"2014-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81544993","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}
We consider the problem of learning an unknown context-free grammar when the only knowledge available and of interest to the learner is about its structural descriptions with depth at most l. The goal is to learn a cover context-free grammar (CCFG) with respect to l, that is, a CFG whose structural descriptions with depth at most l agree with those of the unknown CFG. We propose an algorithm, called LA l, that efficiently learns a CCFG using two types of queries: structural equivalence and structural membership. We show that LA l runs in time polynomial in the number of states of a minimal deterministic finite cover tree automaton (DCTA) with respect to l. This number is often much smaller than the number of states of a minimum deterministic finite tree automaton for the structural descriptions of the unknown grammar.
{"title":"Learning Cover Context-Free Grammars from Structural Data","authors":"M. Marin, Gabriel Istrate","doi":"10.7561/SACS.2014.2.253","DOIUrl":"https://doi.org/10.7561/SACS.2014.2.253","url":null,"abstract":"We consider the problem of learning an unknown context-free grammar when the only knowledge available and of interest to the learner is about its structural descriptions with depth at most l. The goal is to learn a cover context-free grammar (CCFG) with respect to l, that is, a CFG whose structural descriptions with depth at most l agree with those of the unknown CFG. We propose an algorithm, called LA l, that efficiently learns a CCFG using two types of queries: structural equivalence and structural membership. We show that LA l runs in time polynomial in the number of states of a minimal deterministic finite cover tree automaton (DCTA) with respect to l. This number is often much smaller than the number of states of a minimum deterministic finite tree automaton for the structural descriptions of the unknown grammar.","PeriodicalId":53862,"journal":{"name":"Scientific Annals of Computer Science","volume":"116 1","pages":"241-258"},"PeriodicalIF":0.9,"publicationDate":"2014-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77361791","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}
Seeking a general framework for reasoning about and comparing programming languages, we derive a new view of Milner's CCS. We construct a category E of 'plays', and a subcategory V of 'views'. We argue that presheaves on V adequately represent 'innocent' strategies, in the sense of game semantics. We equip innocent strategies with a simple notion of interaction. We then prove decomposition results for innocent strategies, and, restricting to presheaves of finite ordinals, prove that innocent strategies are a final coalgebra for a polynomial functor derived from the game. This leads to a translation of CCS with recursive equations. Finally, we propose a notion of 'interactive equivalence' for innocent strategies, which is close in spirit to Beffara's interpretation of testing equivalences in concurrency theory. In this framework, we consider analogues of fair testing and must testing. We show that must testing is strictly finer in our model than in CCS, since it avoids what we call 'spatial unfairness'. Still, it differs from fair testing, and we show that it coincides with a relaxed form of fair testing.
{"title":"Innocent Strategies as Presheaves and Interactive Equivalences for CCS","authors":"Tom Hirschowitz, D. Pous","doi":"10.4204/EPTCS.59.2","DOIUrl":"https://doi.org/10.4204/EPTCS.59.2","url":null,"abstract":"Seeking a general framework for reasoning about and comparing programming languages, we derive a new view of Milner's CCS. We construct a category E of 'plays', and a subcategory V of 'views'. We argue that presheaves on V adequately represent 'innocent' strategies, in the sense of game semantics. We equip innocent strategies with a simple notion of interaction. We then prove decomposition results for innocent strategies, and, restricting to presheaves of finite ordinals, prove that innocent strategies are a final coalgebra for a polynomial functor derived from the game. This leads to a translation of CCS with recursive equations. Finally, we propose a notion of 'interactive equivalence' for innocent strategies, which is close in spirit to Beffara's interpretation of testing equivalences in concurrency theory. In this framework, we consider analogues of fair testing and must testing. We show that must testing is strictly finer in our model than in CCS, since it avoids what we call 'spatial unfairness'. Still, it differs from fair testing, and we show that it coincides with a relaxed form of fair testing.","PeriodicalId":53862,"journal":{"name":"Scientific Annals of Computer Science","volume":"17 1","pages":"2-24"},"PeriodicalIF":0.9,"publicationDate":"2011-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80769651","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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