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The Power of Programs over Monoids in [chapter]

Nathan Grosshans
2020 Lecture Notes in Computer Science  
In this article, we investigate 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.  ... 
doi:10.1007/978-3-030-40608-0_22 fatcat:yr75pnivlnaotj65el32olchtm

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]

Howard Straubing
2005 Lecture Notes in Computer Science  
Let's start with an especially trivial application 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.  ... 
doi:10.1007/11505877_6 fatcat:i54iyghyjjdz3kahtybm52l6xa

An Algebraic Perspective on Boolean Function Learning [chapter]

Ricard Gavaldà, Denis Thérien
2009 Lecture Notes in Computer Science  
In order to systematize existing results, we propose to analyze 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] .  ... 
doi:10.1007/978-3-642-04414-4_19 fatcat:njs5mutpinberixrcodlezgroe

Non-uniform automata over groups [chapter]

David A. Barrington, Denis Thérien
1987 Lecture Notes in Computer Science  
ACKNOWLEDGMENTS We thank Pierre McKenzie, who first noted 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.  ... 
doi:10.1007/3-540-18088-5_13 fatcat:l6yk5ubxcjdwxadqqhaunjs4fq

Non-uniform automata over groups

David A. Mix Barrington, Howard Straubing, Denis Thérien
1990 Information and Computation  
ACKNOWLEDGMENTS We thank Pierre McKenzie, who first noted 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.  ... 
doi:10.1016/0890-5401(90)90007-5 fatcat:wzfnbwt355gnboq5ti6nxdxvoe

Weighted Tree Automata over Valuation Monoids and Their Characterization by Weighted Logics [chapter]

Manfred Droste, Doreen Götze, Steffen Märcker, Ingmar Meinecke
2011 Lecture Notes in Computer Science  
For bi-locally 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."  ... 
doi:10.1007/978-3-642-24897-9_2 fatcat:4n5wn54jajbw7idpl4irzs6w34

Freyd categories are Enriched Lawvere Theories

Sam Staton
2014 Electronical Notes in Theoretical Computer Science  
On 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'.  ... 
doi:10.1016/j.entcs.2014.02.010 fatcat:cln6hk5jqrc7pfzyyzgmpq4hoe

Languages Defined with Modular Counting Quantifiers

Howard Straubing
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.  ... 
doi:10.1006/inco.2000.2923 fatcat:oc5wtxnb55gezezhx66qofl2oi

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

Pierre Péladeau, Howard Straubing, Denis Therien
1997 Theoretical Computer Science  
We study 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.  ... 
doi:10.1016/s0304-3975(96)00297-6 fatcat:3jt24j2b7rdcxinfyswc4pfnqy

MONOIDS AND COMPUTATIONS

PASCAL TESSON, DENIS THÉRIEN
2004 International journal of algebra and computation  
This contribution wishes to argue in favour 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.  ... 
doi:10.1142/s0218196704001979 fatcat:4seevgcz5jf37ebhtonfik4xku

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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