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The Power of Programs over Monoids in
[chapter]

2020
*
Lecture Notes in Computer Science
*

In this article, we investigate

doi:10.1007/978-3-030-40608-0_22
fatcat:yr75pnivlnaotj65el32olchtm
*the**computational**power**of**programs**over**monoids*in J, a small variety*of**finite*aperiodic*monoids*. ...*The*model*of**programs**over*(*finite*)*monoids*, introduced by Barrington and Thérien, gives an interesting way to characterise*the*circuit complexity class NC 1 and its subclasses and showcases deep connections ...*The*author thanks*the*anonymous referees for their helpful comments and suggestions. ...##
###
Page 8172 of Mathematical Reviews Vol. , Issue 2004j
[page]

2004
*
Mathematical Reviews
*

{For

*the*entire collection see MR 2004h:68006. } 2004j:68126 68Q70 20M35 68Q45 Tesson, Pascal (3-MGL-C; Montreal, QC); Thérien, Denis (3-MGL-C; Montreal, QC)*The**computing**power**of**programs**over**finite*... Let M bea*finite**monoid*. An n-input M-*program**of*length s*over*a*finite*input alphabet A consists*of*an accepting subset F*of*M and a sequence*of*instructions y = (i), f,)... ...##
###
Inexpressibility Results for Regular Languages in Nonregular Settings
[chapter]

2005
*
Lecture Notes in Computer Science
*

Let's start with an especially trivial application

doi:10.1007/11505877_6
fatcat:i54iyghyjjdz3kahtybm52l6xa
*of**the*syntactic*monoid*: Let Σ = {0, 1}, and consider*the*two languages L 1 = {w ∈ Σ * : |w| ≡ 0 (mod 2)} and L 2 = {w ∈ Σ * : |w| 1 ≡ 0 (mod 2)}. ...*Programs**over**Finite**Monoids**The*results*of**the*last section are due to Barrington and Straubing [5] .*The*"nonuniform automata" we considered are special cases*of**programs**over**finite**monoids*. ... Completing this*program*would extend*the*application*of**finite*semigroups in*computation*well beyond*the*domain*of**finite*automata. ...##
###
An Algebraic Perspective on Boolean Function Learning
[chapter]

2009
*
Lecture Notes in Computer Science
*

In order to systematize existing results, we propose to analyze

doi:10.1007/978-3-642-04414-4_19
fatcat:njs5mutpinberixrcodlezgroe
*the*learnability*of*boolean functions*computed*by an algebraically defined model,*programs**over**monoids*. ...*The*expressiveness*of**the*model, hence its learning complexity, depends on*the*algebraic structure*of**the*chosen*monoid*. ... We adopt*the**program**over*a*monoid*as*computing*model*of*Boolean functions [Bar89, BST90] . ...##
###
Non-uniform automata over groups
[chapter]

1987
*
Lecture Notes in Computer Science
*

ACKNOWLEDGMENTS We thank Pierre McKenzie, who first noted

doi:10.1007/3-540-18088-5_13
fatcat:l6yk5ubxcjdwxadqqhaunjs4fq
*the*connections between our efforts and organized*the*meeting in Montreal where we obtained*the*first*of*these results. ... We also thank Martin Cohn, Mike Sipser, and Roman Smolensky for helpful discussions, and*the*referees for several helpful comments. ... Our basic object*of*study is a*program*family*over*a particular*finite**monoid*. ...##
###
Non-uniform automata over groups

1990
*
Information and Computation
*

ACKNOWLEDGMENTS We thank Pierre McKenzie, who first noted

doi:10.1016/0890-5401(90)90007-5
fatcat:wzfnbwt355gnboq5ti6nxdxvoe
*the*connections between our efforts and organized*the*meeting in Montreal where we obtained*the*first*of*these results. ... We also thank Martin Cohn, Mike Sipser, and Roman Smolensky for helpful discussions, and*the*referees for several helpful comments. ... Our basic object*of*study is a*program*family*over*a particular*finite**monoid*. ...##
###
Weighted Tree Automata over Valuation Monoids and Their Characterization by Weighted Logics
[chapter]

2011
*
Lecture Notes in Computer Science
*

For bi-locally

doi:10.1007/978-3-642-24897-9_2
fatcat:4n5wn54jajbw7idpl4irzs6w34
*finite*bimonoids, we show that weighted tree automata capture*the*expressive*power**of*several semantics*of*full weighted MSO logic. Decision procedures follow as consequences. ... We establish a characterization*of**the*behaviors*of*these weighted*finite*tree automata by fragments*of*weighted monadic second-order logic. ... [. . . ] And*of*course, these very same terms make up*the*bulk, if not all,*of*modern*programming*languages." ...##
###
Freyd categories are Enriched Lawvere Theories

2014
*
Electronical Notes in Theoretical Computer Science
*

On

doi:10.1016/j.entcs.2014.02.010
fatcat:cln6hk5jqrc7pfzyyzgmpq4hoe
*the*other hand,*the*notion*of*Freyd category arose in*the*work*of*Levy,*Power*and Thielecke [19, 33] as a categorical framework for first order effectful*programs*. ... When V = Set, 'finitary' means*finite*.*Power*takes V to be a locally*finitely*presentable category, and 'finitary' means*finitely*presentable. ... Acknowledgement It has been helpful about this topic with many people*over**the*years, including This research has been supported by ERC Grant 'Quantum*Computation*, Logic, and Security'. ...##
###
Languages Defined with Modular Counting Quantifiers

2001
*
Information and Computation
*

*The*argument introduces some new techniques, based on a combination

*of*semigroup theory and Ramsey theory, which may shed some light on

*the*general case. C ... We prove that a regular language defined by a boolean combination

*of*generalized 1 -sentences built using modular counting quantifiers can be defined by a boolean combination

*of*1 -sentences in which only ...

*The*

*Computing*

*Power*

*of*k-

*Programs*

*over*Commutative

*Monoids*In this subsection we state a technical lemma about

*the*

*computing*

*power*

*of*k-

*programs*

*over*

*finite*commutative

*monoids*. ...

##
###
Page 2388 of Mathematical Reviews Vol. , Issue 2002D
[page]

2002
*
Mathematical Reviews
*

*The*article gives a survey

*of*various applications

*of*this concept

*of*

*power*algebras in areas such as graph theory, idempotent analysis, dynamic

*programming*and optimization. ... By a

*power*algebra

*over*F

*the*author means

*the*set F4

*of*all mappings from a set A into F together with suitable operations which may be defined with

*the*help

*of*additional properties

*of*A. ...

##
###
Page 5115 of Mathematical Reviews Vol. , Issue 911
[page]

1991
*
Mathematical Reviews
*

This paper is part

*of*a continuing*program*to study*the*connection between languages recognized by*finite*-state automata and*the*algebraic structure*of**the*syntactic*monoid*(i.e.,*the**monoid**of*transitions ... (F-PARIS6-C) On*the*varieties*of*languages associated with some varieties*of**finite**monoids*with commuting idempotents. Inform. and*Comput*. 86 (1990), no. 1, 32-42. ...##
###
Finite semigroup varieties defined by programs

1997
*
Theoretical Computer Science
*

We study

doi:10.1016/s0304-3975(96)00297-6
fatcat:3jt24j2b7rdcxinfyswc4pfnqy
*the*regular languages recognized by polynomial-length*programs**over**finite*semigroups belonging to product varieties V + LI, where V is a variety*of**finite**monoids*, and LI is*the*variety*of**finite*... In*the*case where*the*semigroup variety has a particular closure property with respect to*programs*, we are able to give precise characterizations*of*these regular languages. ... [lo] show that*the**power**of*polynomial-size*programs**over*a class*of**monoids*is essentially captured by*the*regular languages recognized by such*programs*. Barrington et al. ...##
###
MONOIDS AND COMPUTATIONS

2004
*
International journal of algebra and computation
*

This contribution wishes to argue in favour

doi:10.1142/s0218196704001979
fatcat:4seevgcz5jf37ebhtonfik4xku
*of*increased interaction between experts on*finite**monoids*and specialists*of*theory*of**computation*. ... Developing*the*algebraic approach to formal*computations*as well as*the**computational*point*of*view on*monoids*will prove to be beneficial to both communities. ... number*of*interesting questions about AC 0 and*the**computing**power**of**programs**over*aperiodic*monoids*are also left open. Let us denote by AC 0 i*the*class*of*AC 0 circuits*of*depth at most i. ...##
###
Page 1578 of Mathematical Reviews Vol. , Issue 80D
[page]

1980
*
Mathematical Reviews
*

A num- ber

*of*characterizations*of**the*rational subsets*of**the*product X* xX Y**of*a pair*of**finitely*generated free*monoids*are included. ... If X is an alphabet, X* is*the*free ©*monoid**over*X and A is a subset*of*X*, then*the*submonoid*of*X* generated by A is denoted by A *. ...##
###
Page 8771 of Mathematical Reviews Vol. , Issue 99m
[page]

1999
*
Mathematical Reviews
*

, Krzysztof (PL-WROC-C; Wroclaw)

*Power**of*cooperation and multihead*finite*systems. ... Finally*the*problem*of*deciding algebraic properties*of**the**monoid*presented by a*finite*For*the*web version*of*Mathematical Reviews, see http: //www.ams.org/mathscinet ...
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