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On the Learnability of Infinitary Regular Sets

1995
*
Information and Computation
*

In this paper we extend

doi:10.1006/inco.1995.1070
fatcat:jmekb52g65c3xjjamr4p4tx5p4
*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. ...##
###
On the Learnability of Infinitary Regular Sets
[chapter]

1991
*
COLT
*

In this paper we extend

doi:10.1016/b978-1-55860-213-7.50015-8
fatcat:mb2ntao6hzci5bzjwp7y5zak4i
*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. ...##
###
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

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. ...

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

2012
*
arXiv
*
pre-print

By reformulating a learning process

arXiv:1112.2801v3
fatcat:yipvi2he3vfxnaurgbrpcnouu4
*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). ...##
###
Bounds in Query Learning
[article]

2019
*
arXiv
*
pre-print

Our approach is flexible and powerful enough to enough to give new and very short proofs

arXiv:1904.10122v1
fatcat:krahhqavrbdrtfcx3wjej3wtoe
*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. ...##
###
A new order theory of set systems and better quasi-orderings

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). ...

##
###
On the Necessity of U-Shaped Learning

2013
*
Topics in Cognitive Science
*

We present results about

doi:10.1111/tops.12002
pmid:23335574
fatcat:l7wgkacx75asvoelwqohjs7wzu
*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. ...##
###
Inside the Muchnik degrees II: The degree structures induced by the arithmetical hierarchy of countably continuous functions

2014
*
Annals of Pure and Applied Logic
*

We shed light

doi:10.1016/j.apal.2014.03.001
fatcat:xyn6jp6yureq3lql4hpfvcndbi
*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. ...##
###
Inside the Muchnik Degrees I: Discontinuity, Learnability, and Constructivism
[article]

2013
*
arXiv
*
pre-print

For instance, we show that mind-change-bounded-

arXiv:1210.0697v2
fatcat:fzwfvaz6rramlmje3q7bi23a44
*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. ...##
###
Automated assume-guarantee reasoning for omega-regular systems and specifications

2011
*
Innovations in Systems and Software Engineering
*

We study

doi:10.1007/s11334-011-0148-1
fatcat:mozrp3cw3jgxpluvj2622bdhze
*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 . ...##
###
Inside the Muchnik Degrees II: The Degree Structures induced by the Arithmetical Hierarchy of Countably Continuous Functions
[article]

2013
*
arXiv
*
pre-print

We shed light

arXiv:1309.1937v1
fatcat:66snlizce5dhlayfqnajbnyr74
*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. ...##
###
Generalizing over Several Learning Settings
[chapter]

2010
*
Lecture Notes in Computer Science
*

We present a meta-algorithm that generalizes over as many

doi:10.1007/978-3-642-15488-1_28
fatcat:hfjjdztaljd6rgid4pbyc5psdq
*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*. ...##
###
Open Problems in Logical Dynamics
[chapter]

2006
*
Mathematical Problems from Applied Logic I
*

Eventually, this calls for a merge

doi:10.1007/0-387-31072-x_3
fatcat:f5il7g4k6zcdndjrl3ymqaetl4
*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.) ...
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