{"title":"Learning of Structurally Unambiguous Probabilistic Grammars","authors":"Dolav Nitay, D. Fisman, Michal Ziv-Ukelson","doi":"10.46298/lmcs-19(1:10)2023","DOIUrl":"https://doi.org/10.46298/lmcs-19(1:10)2023","url":null,"abstract":"The problem of identifying a probabilistic context free grammar has two aspects: the first is determining the grammar's topology (the rules of the grammar) and the second is estimating probabilistic weights for each rule. Given the hardness results for learning context-free grammars in general, and probabilistic grammars in particular, most of the literature has concentrated on the second problem. In this work we address the first problem. We restrict attention to structurally unambiguous weighted context-free grammars (SUWCFG) and provide a query learning algorithm for strucuturally unambiguous probabilistic context-free grammars (SUPCFG). We show that SUWCFG can be represented using co-linear multiplicity tree automata (CMTA), and provide a polynomial learning algorithm that learns CMTAs. We show that the learned CMTA can be converted into a probabilistic grammar, thus providing a complete algorithm for learning a strucutrally unambiguous probabilistic context free grammar (both the grammar topology and the probabilistic weights) using structured membership queries and structured equivalence queries. We demonstrate the usefulness of our algorithm in learning PCFGs over genomic data.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129269096","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":"Inferring Symbolic Automata","authors":"D. Fisman, Hadar Frenkel, Sandra Zilles","doi":"10.4230/LIPIcs.CSL.2022.21","DOIUrl":"https://doi.org/10.4230/LIPIcs.CSL.2022.21","url":null,"abstract":"We study the learnability of symbolic finite state automata (SFA), a model\u0000shown useful in many applications in software verification. The\u0000state-of-the-art literature on this topic follows the query learning paradigm,\u0000and so far all obtained results are positive. We provide a necessary condition\u0000for efficient learnability of SFAs in this paradigm, from which we obtain the\u0000first negative result. The main focus of our work lies in the learnability of\u0000SFAs under the paradigm of identification in the limit using polynomial time\u0000and data, and its strengthening efficient identifiability, which are concerned\u0000with the existence of a systematic set of characteristic samples from which a\u0000learner can correctly infer the target language. We provide a necessary\u0000condition for identification of SFAs in the limit using polynomial time and\u0000data, and a sufficient condition for efficient learnability of SFAs. From these\u0000conditions we derive a positive and a negative result. The performance of a\u0000learning algorithm is typically bounded as a function of the size of the\u0000representation of the target language. Since SFAs, in general, do not have a\u0000canonical form, and there are trade-offs between the complexity of the\u0000predicates on the transitions and the number of transitions, we start by\u0000defining size measures for SFAs. We revisit the complexity of procedures on\u0000SFAs and analyze them according to these measures, paying attention to the\u0000special forms of SFAs: normalized SFAs and neat SFAs, as well as to SFAs over a\u0000monotonic effective Boolean algebra. This is an extended version of the paper\u0000with the same title published in CSL'22.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122490454","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 categorical framework for congruence of applicative bisimilarity in higher-order languages","authors":"Tom Hirschowitz, Ambroise Lafont","doi":"10.46298/lmcs-18(3:37)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(3:37)2022","url":null,"abstract":"Applicative bisimilarity is a coinductive characterisation of observational equivalence in call-by-name lambda-calculus, introduced by Abramsky (1990). Howe (1996) gave a direct proof that it is a congruence, and generalised the result to all languages complying with a suitable format. We propose a categorical framework for specifying operational semantics, in which we prove that (an abstract analogue of) applicative bisimilarity is automatically a congruence. Example instances include standard applicative bisimilarity in call-by-name, call-by-value, and call-by-name non-deterministic $lambda$-calculus, and more generally all languages complying with a variant of Howe's format.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117211739","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":"Concurrent Process Histories and Resource Transducers","authors":"Chad Nester","doi":"10.46298/lmcs-19(1:7)2023","DOIUrl":"https://doi.org/10.46298/lmcs-19(1:7)2023","url":null,"abstract":"We identify the algebraic structure of the material histories generated by\u0000concurrent processes. Specifically, we extend existing categorical theories of\u0000resource convertibility to capture concurrent interaction. Our formalism admits\u0000an intuitive graphical presentation via string diagrams for proarrow\u0000equipments. We also consider certain induced categories of resource\u0000transducers, which are of independent interest due to their unusual structure.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125124755","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 Nielsen-Schreier Theorem in Homotopy Type Theory","authors":"Andrew W. Swan","doi":"10.46298/lmcs-18(1:18)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(1:18)2022","url":null,"abstract":"We give a formulation of the Nielsen-Schreier theorem (subgroups of free groups are free) in homotopy type theory using the presentation of groups as pointed connected 1-truncated types. We show the special case of finite index subgroups holds constructively and the full theorem follows from the axiom of choice. We give an example of a boolean infinity topos where our formulation of the theorem does not hold and show a stronger \"untruncated\" version of the theorem is provably false in homotopy type theory.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124803715","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}
Thomas Brihaye, G. Geeraerts, A. Haddad, Engel Lefaucheux, B. Monmege
{"title":"One-Clock Priced Timed Games with Negative Weights","authors":"Thomas Brihaye, G. Geeraerts, A. Haddad, Engel Lefaucheux, B. Monmege","doi":"10.46298/lmcs-18(3:17)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(3:17)2022","url":null,"abstract":"Priced timed games are two-player zero-sum games played on priced timed\u0000automata (whose locations and transitions are labeled by weights modelling the\u0000cost of spending time in a state and executing an action, respectively). The\u0000goals of the players are to minimise and maximise the cost to reach a target\u0000location, respectively. We consider priced timed games with one clock and\u0000arbitrary integer weights and show that, for an important subclass of them (the\u0000so-called simple priced timed games), one can compute, in pseudo-polynomial\u0000time, the optimal values that the players can achieve, with their associated\u0000optimal strategies. As side results, we also show that one-clock priced timed\u0000games are determined and that we can use our result on simple priced timed\u0000games to solve the more general class of so-called negative-reset-acyclic\u0000priced timed games (with arbitrary integer weights and one clock). The\u0000decidability status of the full class of priced timed games with one-clock and\u0000arbitrary integer weights still remains open.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127742806","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}
Daniel Carranza, Jonathan Chang, Chris Kapulkin, Ryan Sandford
{"title":"2-adjoint Equivalences in Homotopy Type Theory","authors":"Daniel Carranza, Jonathan Chang, Chris Kapulkin, Ryan Sandford","doi":"10.23638/LMCS-17(1:3)2021","DOIUrl":"https://doi.org/10.23638/LMCS-17(1:3)2021","url":null,"abstract":"We introduce the notion of (half) 2-adjoint equivalences in Homotopy Type Theory and prove their expected properties. We formalized these results in the Lean Theorem Prover.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114981217","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 Taylor expansion of λ-terms and the groupoid structure of their rigid approximants","authors":"Federico Olimpieri, Lionel Vaux Auclair","doi":"10.46298/lmcs-18(1:1)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(1:1)2022","url":null,"abstract":"We show that the normal form of the Taylor expansion of a $lambda$-term is\u0000isomorphic to its B\"ohm tree, improving Ehrhard and Regnier's original proof\u0000along three independent directions. First, we simplify the final step of the\u0000proof by following the left reduction strategy directly in the resource\u0000calculus, avoiding to introduce an abstract machine ad hoc. We also introduce a\u0000groupoid of permutations of copies of arguments in a rigid variant of the\u0000resource calculus, and relate the coefficients of Taylor expansion with this\u0000structure, while Ehrhard and Regnier worked with groups of permutations of\u0000occurrences of variables. Finally, we extend all the results to a\u0000nondeterministic setting: by contrast with previous attempts, we show that the\u0000uniformity property that was crucial in Ehrhard and Regnier's approach can be\u0000preserved in this setting.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"203 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123967498","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":"Duality for powerset coalgebras","authors":"G. Bezhanishvili, L. Carai, P. Morandi","doi":"10.46298/lmcs-18(1:27)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(1:27)2022","url":null,"abstract":"Let CABA be the category of complete and atomic boolean algebras and complete\u0000boolean homomorphisms, and let CSL be the category of complete\u0000meet-semilattices and complete meet-homomorphisms. We show that the forgetful\u0000functor from CABA to CSL has a left adjoint. This allows us to describe an\u0000endofunctor H on CABA such that the category Alg(H) of algebras for H is dually\u0000equivalent to the category Coalg(P) of coalgebras for the powerset endofunctor\u0000P on Set. As a consequence, we derive Thomason duality from Tarski duality,\u0000thus paralleling how J'onsson-Tarski duality is derived from Stone duality.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"29 56","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134505123","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 Expressive Power of Higher-Order Pushdown Systems","authors":"P. Parys","doi":"10.23638/LMCS-16(3:11)2020","DOIUrl":"https://doi.org/10.23638/LMCS-16(3:11)2020","url":null,"abstract":"We show that deterministic collapsible pushdown automata of second order can recognize a language that is not recognizable by any deterministic higher-order pushdown automaton (without collapse) of any order. This implies that there exists a tree generated by a second order collapsible pushdown system (equivalently, by a recursion scheme of second order) that is not generated by any deterministic higher-order pushdown system (without collapse) of any order (equivalently, by any safe recursion scheme of any order). As a side effect, we present a pumping lemma for deterministic higher-order pushdown automata, which potentially can be useful for other applications.","PeriodicalId":314387,"journal":{"name":"Log. Methods Comput. Sci.","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134461670","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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