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An Algebraic Characterization of Strictly Piecewise Languages [chapter]

Jie Fu, Jeffrey Heinz, Herbert G. Tanner
2011 Lecture Notes in Computer Science  
The algebraic characterization highlights a similarity between the Strictly Piecewise and Strictly Local languages, and also leads to a procedure which can decide whether a regular language L is Strictly  ...  Piecewise in polynomial time in the size of the syntactic monoid for L.  ...  Also, the algebraic characterization for SP provides a polynomial-time decision procedure for a regular language in the size of its syntactic monoid.  ... 
doi:10.1007/978-3-642-20877-5_26 fatcat:pudolioeg5e2rkeoxtrvftdtuy

Page 4352 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews  
A semigroup S is strongly locally testable if it is strongly k-testable for some k > 1. For finite semigroups, x® denotes the unique power of x that is idempotent.  ...  The algebra is distinguished by the design decision that it only allows actions to pre-empt others at the same ‘location’ and there- fore captures a notion of localized precedence.  ... 

Page 261 of Mathematical Reviews Vol. , Issue 85a [page]

1985 Mathematical Reviews  
., TIL schemes] are identified with certain RL schemes for which RF is a strictly locally testable language [resp., a finite union of strictly locally testable languages].  ...  Using the virtual identity of RL schemes with a-transducers, a collection of decision procedures are imported into L theory from the theory of a-transducers.  ... 

Page 6034 of Mathematical Reviews Vol. , Issue 88k [page]

1988 Mathematical Reviews  
(The corresponding proper- ties of languages are: rational, star-free, piecewise testable, endwise testable, and locally testable.)  ...  Summary: “The Knuth-Bendix procedure for word problems in universal algebra is known to be very effective when it is applica- ble.  ... 

Quantum probability and quantum decision making [article]

V.I. Yukalov, D. Sornette
2016 arXiv   pre-print
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements  ...  Conditions are formulated for the case when quantum decision theory reduces to its classical counterpart and for the situation where the use of quantum decision theory is necessary.  ...  Yukalova for discussions. Funding: Financial support from the Swiss National Foundation is appreciated.  ... 
arXiv:1601.02480v1 fatcat:nkeajivmc5ezbjrgyvnfrj5qvu

Quantum probability and quantum decision-making

V. I. Yukalov, D. Sornette
2015 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
Let A = {Â} be an algebra of local observables defined on a Hilbert space H A .  ...  Observable quantities in quantum theory are represented by self-adjoint operators, sayÂ, from the algebra of local observables.  ...  Yukalova for discussions.  ... 
doi:10.1098/rsta.2015.0100 pmid:26621989 fatcat:6f7dustp5ncp5mqsksadcpjaba

A characterization of strictly locally testable languages and its application to subsemigroups of a free semigroup

Aldo De Luca, Antonio Restivo
1980 Information and Control  
This condition gives then an algebraic decision procedure for strictly local 300  ...  The characterization of strictly locally subsets X of A + is that X is strictly locally testable if and only if all the sufficiently long words of A-are constants for X.  ...  Proposition 2.1 is of great interest since it gives, being S(X) finite, an algebraic decision procedure for local testability.  ... 
doi:10.1016/s0019-9958(80)90180-1 fatcat:pluuy6hcb5gu7blc5z2upf2fzu

Verification Tools for Checking some kinds of Testability [article]

A.N. Trahtman
2021 arXiv   pre-print
A set of procedures for deciding whether or not a language given by its minimal automaton or by its syntactic semigroup is locally testable, right or left locally testable, threshold locally testable,  ...  We consider some approaches to verify these procedures and use for this aim some auxiliary programs.  ...  The package contains a set of procedures for deciding whether or not a language given by its minimal automaton or by its syntactic semigroup is locally testable, right or left locally testable, threshold  ... 
arXiv:2106.02312v1 fatcat:offfcgrr7rbjjp7y6fhhkhyeou

Algebraic recognizability of languages [article]

Pascal Weil
2006 arXiv   pre-print
Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory.  ...  We would like to briefly explore why that is, and how this word-related notion extends to more complex models, such as those developed for modeling distributed or timed behaviors.  ...  This possibility is explicitly stated in Theorem 1.2, but it is also the underlying reason for the decision procedures concerning piecewise testable (Stern [76] ) and locally testable languages (Kim,  ... 
arXiv:cs/0609110v1 fatcat:2fnhr3gu5rdbbdugq76cqfvl4y

Separating Regular Languages by Locally Testable and Locally Threshold Testable Languages

Thomas Place, Lorijn Van Rooijen, Marc Zeitoun, Marc Herbstritt
2013 Foundations of Software Technology and Theoretical Computer Science  
We investigate the following decision problem: given two regular input languages, decide whether there exists a locally testable (resp. a locally threshold testable) separator.  ...  In both cases, we design a decision procedure based on the occurrence of special patterns in automata accepting the input languages.  ...  Locally Threshold Testable Languages.  ... 
doi:10.4230/lipics.fsttcs.2013.363 dblp:conf/fsttcs/PlaceRZ13 fatcat:olpvektv2zbxzk4mkofu6fkpbu

Probabilistically Checkable Proofs and Codes

Irit Dinur
2011 Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)  
First, we describe the related and possibly cleaner problem of constructing locally testable codes. These are essentially error correcting codes that are testable by a randomized local algorithm.  ...  Although the verification is simple, it is not local, i.e., a verifier must typically read (almost) the entire proof in order to reach the right decision.  ...  Acknowledgements I wish to thank Adi Akavia, Elazar Goldenberg, Or Meir, Igor Shinkar and Oded Schwartz for helpful comments.  ... 
doi:10.1142/9789814324359_0013 fatcat:dudwyxj3snerfjreay3bl26b4u

Algebraic Recognizability of Languages [chapter]

Pascal Weil
2004 Lecture Notes in Computer Science  
In this paper, we concentrate on the algebraic notion of recognizability: that which, for finite words, exploits the monoid structure of the set of words, and relies on the consideration of monoid morphisms  ...  timed words, etc) -, and for extending to these models the tools that were developped for words.  ...  This possibility is explicitly stated in Theorem 1.2, but it is also the underlying reason for the decision procedures concerning piecewise testable (Stern [76] ) and locally testable languages (Kim,  ... 
doi:10.1007/978-3-540-28629-5_8 fatcat:5el7wd3umvgdzhw4dxukeugoci

Forest Categories [article]

Howard Straubing
2018 arXiv   pre-print
As an illustration of the usefulness of this method, we provide a new proof of a result of Place and Segoufin characterizing locally testable tree languages.  ...  We extend Tilson's theory of the algebra of finite categories, in particular, the Derived Category Theorem, to the setting of forest algebras.  ...  For local testability, this implies the following: Theorem 8 If L ⊆ H A is locally testable, then it is |H| 2 + 1-locally testable. Proof By hypothesis, L is N -locally testable for some N.  ... 
arXiv:1801.04337v1 fatcat:2ofmsya3w5dphbybv3wzdtvype

An algebraic characterization of frontier testable tree languages

Thomas Wilke
1996 Theoretical Computer Science  
The class of frontier testable (i.e., reverse definite) tree languages is characterized by a !inite set of pseudoidentities for tree algebras, which are introduced here for this characterization.  ...  An efficient algorithm is presented that decides whether a given tree automaton recognizes a frontier testable tree language.  ...  Acknowledgements I thank Magnus Steinby, Andreas Podelski, and the anonymous referee for valuable comments on and corrections of this paper and also its conference version [ 181.  ... 
doi:10.1016/0304-3975(95)00131-x fatcat:5nsyzhg4lbdfbgtwjfkwcknwlq

Testing Assignments to Constraint Satisfaction Problems [article]

Hubie Chen, Matt Valeriote, Yuichi Yoshida
2016 arXiv   pre-print
(ii) Else, if A has a (k + 1)-ary near-unanimity polymorphism for some k ≥ 2, and no Maltsev polymorphism then ∃CSP(A) is not constant-query testable (even with two-sided error) but is sublinear-query  ...  testable with one-sided error.  ...  in the Split procedure.  ... 
arXiv:1608.03017v1 fatcat:znn7lunimnajvgmr4arfqvi3g4
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