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On the Learnability of Infinitary Regular Sets

O. Maler, A. Pnueli
1995 Information and Computation  
In this paper we extend the automaton synthesis paradigm to infinitary languages, that is, to subsets of the set Σ ω of all infinite sequences over some alphabet Σ.  ...  Our main result is a polynomial algorithm for learning a sub-class of the ω-regular sets from membership queries and counter-examples based on the framework suggested by Angluin (Angluin, D., 1987, Information  ...  We thank one anonymous referee for noting a small bug in a previous version of the algorithm, and a second referee for demanding an improvement in the presentation of theorem 10.  ... 
doi:10.1006/inco.1995.1070 fatcat:jmekb52g65c3xjjamr4p4tx5p4

On the Learnability of Infinitary Regular Sets [chapter]

Oded Maler, Amir Pnueli
1991 COLT  
In this paper we extend the automaton synthesis paradigm to infinitary languages, that is, to subsets of the set Σ ω of all infinite sequences over some alphabet Σ.  ...  Our main result is a polynomial algorithm for learning a sub-class of the ω-regular sets from membership queries and counter-examples based on the framework suggested by Angluin (Angluin, D., 1987, Information  ...  We thank one anonymous referee for noting a small bug in a previous version of the algorithm, and a second referee for demanding an improvement in the presentation of theorem 10.  ... 
doi:10.1016/b978-1-55860-213-7.50015-8 fatcat:mb2ntao6hzci5bzjwp7y5zak4i

Page 1918 of Mathematical Reviews Vol. , Issue 97C [page]

1997 Mathematical Reviews  
{For the entire collection see MR 96e:68002. } Wolfgang Thomas (Kiel) 97c:68103 68Q60 03B70 03D05 68T0S Maler, Oded; Pnueli, Amir (IL-WEIZ-AM; Rehovot) On the learnability of infinitary regular sets.  ...  Thus our work is directed toward the generalization of samples consisting of good and bad infinite sequences into w-regular sets.  ... 

Page 4274 of Mathematical Reviews Vol. , Issue 95g [page]

1995 Mathematical Reviews  
The main problem presented in this paper is the learnability of enumerable families of uniformly recursive languages in terms of the number of allowed mind changes.  ...  Applying this measure of efficiency, the authors prove that the class preserving learning al- gorithms are superior to exact learnability.  ... 

Computational learning theory

Dana Angluin
1992 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing - STOC '92  
On the complexity of learning from counterexamples and membership queries. In Proceedings of the 31st Annual Sympoity of infinitary regular sets.  ...  Maler and Pnueli [95] give an efficient algorithm to learn a subclass of the infinitary regular sets using member- ship and equivalence queries.  ... 
doi:10.1145/129712.129746 dblp:conf/stoc/Angluin92 fatcat:7aw3cnd745bellyhu7phywpul4

A new order theory of set systems and better quasi-orderings [article]

Yohji Akama
2012 arXiv   pre-print
By reformulating a learning process of a set system L as a game between Teacher (presenter of data) and Learner (updater of the abstract independent set), we define the order type dim L of L to be the  ...  The characterization shows that the order structure of the set system L with respect to the set-inclusion is not important for the resulting set system having order type.  ...  This work is partially supported by Grant-in-Aid for Scientific Research (C) (21540105) of the Ministry of Education, Culture, Sports, Science and Technology (MEXT).  ... 
arXiv:1112.2801v3 fatcat:yipvi2he3vfxnaurgbrpcnouu4

Bounds in Query Learning [article]

Hunter Chase, James Freitag
2019 arXiv   pre-print
Our approach is flexible and powerful enough to enough to give new and very short proofs of the efficient learnability of several prominent examples (e.g. regular languages and regular ω-languages), in  ...  some cases also producing new bounds on the number of queries.  ...  ) of ω-languages for which an infinitary invariant of the Myhill-Nerode theorem holds.  ... 
arXiv:1904.10122v1 fatcat:krahhqavrbdrtfcx3wjej3wtoe

A new order theory of set systems and better quasi-orderings

Yohji AKAMA
2012 Progress in Informatics  
The characterization shows that the order structure of the set system L with respect to the set inclusion is not important for the resulting set system having order type.  ...  By reformulating a learning process of a set system L as a game between Teacher (presenter of data) and Learner (updater of abstract independent set), we define the order type dim L of L to be the order  ...  This work is partially supported by Grant-in-Aid for Scientific Research (C) (21540105) of the Ministry of Education, Culture, Sports, Science and Technology (MEXT).  ... 
doi:10.2201/niipi.2012.9.3 fatcat:xcqk5yadqzgp7bceqc5oobsb74

On the Necessity of U-Shaped Learning

Lorenzo Carlucci, John Case
2013 Topics in Cognitive Science  
We present results about the necessity of U-shaped learning in classical models of learning as well as in models with bounds on the memory of the learner.  ...  We present and discuss a body of results in the abstract mathematical setting of (extensions of) Gold-style computational learning theory addressing a mathematically precise version of the following question  ...  that the class of regular languages is not learnable in the limit in the explanatory sense.  ... 
doi:10.1111/tops.12002 pmid:23335574 fatcat:l7wgkacx75asvoelwqohjs7wzu

Inside the Muchnik degrees II: The degree structures induced by the arithmetical hierarchy of countably continuous functions

K. Higuchi, T. Kihara
2014 Annals of Pure and Applied Logic  
We shed light on the fine structures inside these Muchnik degrees related to learnability and piecewise computability.  ...  degree containing infinitely many finite-∆ 0 2 -piecewise degrees (where (Π 0 n ) 2 denotes the difference of two Π 0 n sets), whereas the greatest degrees in these three "finite-Γ-piecewise" degree structures  ...  like to thank Makoto Tatsuta and Yoriyuki Yamagata for introducing him to the syntactical study on Limit Computable Mathematics.  ... 
doi:10.1016/j.apal.2014.03.001 fatcat:xyn6jp6yureq3lql4hpfvcndbi

Inside the Muchnik Degrees I: Discontinuity, Learnability, and Constructivism [article]

Kojiro Higuchi, Takayuki Kihara
2013 arXiv   pre-print
For instance, we show that mind-change-bounded-learnability is equivalent to finite (Π^0_1)_2-piecewise computability (where (Π^0_1)_2 denotes the difference of two Π^0_1 sets), error-bounded-learnability  ...  To develop computability theory of discontinuous functions, we study low levels of the arithmetical hierarchy of nonuniformly computable functions on Baire space.  ...  The second author also would like to thank Makoto Tatsuta and Yoriyuki Yamagata for introducing him to the syntactical study on Limit Computable Mathematics.  ... 
arXiv:1210.0697v2 fatcat:fzwfvaz6rramlmje3q7bi23a44

Automated assume-guarantee reasoning for omega-regular systems and specifications

Sagar Chaki, Arie Gurfinkel
2011 Innovations in Systems and Software Engineering  
We study the applicability of non-circular (AG-NC) and circular (AG-C) AG proof rules in the context of systems with infinite behaviors.  ...  We present a general formalization, called LAG, of the learning based automated AG paradigm. We show how existing approaches for automated AG reasoning are special instances of LAG.  ...  The language accepted by A, L(A), is the set of all words w ∈ Σ * s.t. there exists a run r of w on A, with First(r) ∈ Init ∧Last(r) ∈ F .  ... 
doi:10.1007/s11334-011-0148-1 fatcat:mozrp3cw3jgxpluvj2622bdhze

Inside the Muchnik Degrees II: The Degree Structures induced by the Arithmetical Hierarchy of Countably Continuous Functions [article]

Kojiro Higuchi, Takayuki Kihara
2013 arXiv   pre-print
We shed light on the fine structures inside these Muchnik degrees related to learnability and piecewise computability.  ...  containing infinitely many finite-Δ^0_2-piecewise degrees (where (Π^0_n)_2 denotes the difference of two Π^0_n sets), whereas the greatest degrees in these three "finite-Γ-piecewise" degree structures  ...  like to thank Makoto Tatsuta and Yoriyuki Yamagata for introducing him to the syntactical study on Limit Computable Mathematics.  ... 
arXiv:1309.1937v1 fatcat:66snlizce5dhlayfqnajbnyr74

Generalizing over Several Learning Settings [chapter]

Anna Kasprzik
2010 Lecture Notes in Computer Science  
We present a meta-algorithm that generalizes over as many settings involving one or more of those information sources as possible and covers the whole range of combinations allowing inference with polynomial  ...  We recapitulate regular one-shot learning from membership and equivalence queries, positive and negative finite data.  ...  However, see [13] for an incremental RPNI, and [14] for learning from a stream of labeled examples and MQs. Maler, O., Pnueli, A.: On the learnability of infinitary regular sets.  ... 
doi:10.1007/978-3-642-15488-1_28 fatcat:hfjjdztaljd6rgid4pbyc5psdq

Open Problems in Logical Dynamics [chapter]

Johan van Benthem
2006 Mathematical Problems from Applied Logic I  
Eventually, this calls for a merge of epistemic and a temporal logic which allows for statements of regularities over time, often in the form of 'protocols' (Section 7).  ...  In this survey, the main emphasis will be on the first type of question, but there are a few of the second kind as well. We only mention issues of the third kind in passing. Finally, a caveat.  ...  (Cf. also van der Meiden 1998 on looking for regular subcases of temporal run models where anything goes.)  ... 
doi:10.1007/0-387-31072-x_3 fatcat:f5il7g4k6zcdndjrl3ymqaetl4
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