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The topologies of sofic subshifts have computable Pierce invariants

Tom Head
1991 RAIRO - Theoretical Informatics and Applications  
Starting from an automaton that recognizes the language of fragments of S we construct a second automaton which recognizes a regular language that has as its adhérence a topological space that is homeomorphic  ...  Nivat made systematic use of topological concepts in formai language theory in [2] where they defmed and studied what is called the adhérence of a language.  ... 
doi:10.1051/ita/1991250302471 fatcat:t5l6gclgmze73eif2ny2zlhmbi

The topological structure of adherences of regular languages

Tom Head
1986 RAIRO - Theoretical Informatics and Applications  
ACKNOWLEDGMENT The author wishes to express his thanks to his colleague Robert Piacenza for valuable conversations concerning topological questions and particularly for pointing out the Memoir by R.  ...  In Theorem 1 the topological spaces that arise as adhérences of arbitrary languages are characterized abstractly as the zero-dimensional compact metrizable spaces and concretely as the closed subspaces  ...  Pierce has defined and studied zero-dimensional compact metric spaces of finite type in [5] . This is exactly the class of spaces that arise as adhérences of regular languages.  ... 
doi:10.1051/ita/1986200100311 fatcat:z6r2s23tpverdb6sdxhpebxue4

Subword topology

V.Rajkumar Dare, Rani Siromoney
1986 Theoretical Computer Science  
Well-known topological concepts such as compactness, closure of a language and closed sets reflect certain characteristic properties of subwords.  ...  The familiar topological concept of closure leads us to define the notion of S-adherence (subword adherence) similar to the concept of adherence introduced by Nivat [6].  ...  In a topological space X, the closure of a set L is defined as /S = {x ~ X: every neighbourhood of x intersects L}.  ... 
doi:10.1016/0304-3975(86)90143-x fatcat:cgsl6biaxbf3nnpq2ufm53xlfe

Page 4500 of Mathematical Reviews Vol. , Issue 87h [page]

1987 Mathematical Reviews  
of languages as topological spaces.  ...  The general study of the topological structure of adherences of languages can be shown to be equivalent to the study of the structure of zero-dimensional compact metric spaces.  ... 

Topology on words

Cristian S. Calude, Helmut Jürgensen, Ludwig Staiger
2009 Theoretical Computer Science  
By comparing the resulting topologies and their implied concepts of limit, adherence, continuity and so on, we expect to uncover general properties of topologies on words.  ...  The guiding example is the topology generated by the prefix relation on the set of finite words, considered as a partial order.  ...  Acknowledgement This research was supported in part by the Natural Sciences and Engineering Research Council of Canada.  ... 
doi:10.1016/j.tcs.2009.02.029 fatcat:ho6ixqxlnre2lnq3tbqabbxe2i

Infinite arrays and infinite computations

Rani Siromoney, V.Rajkumar Dare, K.R. Subramanian
1983 Theoretical Computer Science  
A complete metric ttipology is introduced on the set of :il finite and infinite arrays and the topological properties of the space are studied.  ...  For this class, the finite array language generated by a reduced grammar in Greibach normal form and the set of infinite arrays generated bv it are related through the notion of adherence.  ...  Acknowledgment The authors thank the referees for their useful comments.  ... 
doi:10.1016/0304-3975(83)90049-x fatcat:zyvrqe3mt5gqralm3olhuqg7qa

Page 2094 of Mathematical Reviews Vol. , Issue 88d [page]

1988 Mathematical Reviews  
Adherences of languages are characterized topologically as fol- lows: A topological space S is homeomorphic with Adh L for some A and LC A®* if and only if S is homeomorphic with a closed subset of the  ...  Christine Charretton (Villeurbanne) 88d:68052 68045 Head, Tom (1-AK) The topological structure of adherences of regular languages. (French summary) RAIRO Inform. Théor. Appl. 20 (1986), no. 1, 31-41.  ... 

A Topological Sorites

Zach Weber, Mark Colyvan
2010 Journal of Philosophy  
This property can be expressed with the notion of metric adherence (where topological adherence is defined in section iv below): A point x is adherent to a set X iff for any e, no matter how small, the  ...  Be that as it may, the underlying space here is continuous (putting aside, for the purposes of argument, debates about the discreteness or continuity of space-time).  ... 
doi:10.5840/jphil2010107624 fatcat:64ufeaf6ojewbnc3yqp5lq26lu

Page 5729 of Mathematical Reviews Vol. , Issue 92j [page]

1992 Mathematical Reviews  
Starting from an automaton that recognizes the language of fragments of S, we construct a second automaton which recognizes a regular language that has as its adherence a topological space that is homeomorphic  ...  With each such space he associated a finitary invariant that characterized the structure of the space. We show that the topology of each sofic subshift S is of finite type in the sense of Pierce.  ... 

Languages and semantics of grammatical discrete structures

1999 Artificial intelligence for engineering design, analysis and manufacturing  
This paper explores structural design languages and semantics for the generation of feasible and purposeful discrete structures.  ...  Explicit domain knowledge is placed within the grammar through rule and syntax formulation, resulting in the generation of only forms that make functional sense and adhere to preferred visual styles.  ...  ACKNOWLEDGMENTS The authors acknowledge the National Science Foundation under grants EID-9256665, DDM-9300196, and DDM-9258090 and the Engineering Design Research Center, an NSF research center at Carnegie  ... 
doi:10.1017/s0890060499134012 fatcat:mitxvg4ngncvzbhuspohwq77ti


1967 General Topology and its Relations to Modern Analysis and Algebra  
adherence of set A appears to be nothing but the adherence of the associated principal filter jj/1, Z], and operator si: <P(X) -» ty(X) as an extension of operator C : ty(X) -+ *$(X).  ...  The translation of multiplication of pretopologies into the languages si and JS?  ... 
doi:10.1016/b978-1-4831-9850-7.50078-3 fatcat:rdtm32gspnc4bcnikhhfkr5jqq


S. Salleh, U. Ujang, S. Azri
2021 The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences  
Parallel to how geometries describe the shape of an object, topological information is also an important spatial property which describes how the geometries in a space are related to each other.  ...  This paper provided an overview on the current implementations of topological support in spatial databases such as ArcGIS, QGIS, PostgreSQL and others.  ...  ACKNOWLEGEMENTS This research was supported by Ministry of Education (MOE) through Fundamental Research Grant Scheme (FRGS/1/2021/WAB07/UTM/02/2).  ... 
doi:10.5194/isprs-archives-xlvi-4-w5-2021-473-2021 fatcat:7lx5hdl53rhilhxksnreit3lnu

Formal Languages in Dynamical Systems [article]

G. Troll
1993 arXiv   pre-print
The Chomsky hierarchy measuring the complexity of formal languages can be transferred via either of these functors from formal languages to symbolic dynamics and proves to be a conjugacy invariant there  ...  This functor additionally maps topological conjugacies between subshifts to empty-string-limited generalized sequential machines between languages.  ...  Acknowledgement This paper was presented at the 21st Winter School of the Charles University, Prague, on Abstract Analysis, Section Topology, Jan. 23 -30, 1993.  ... 
arXiv:chao-dyn/9305008v1 fatcat:76adb5fhyvbghp472n6t7ba5by

Page 350 of Mathematical Reviews Vol. , Issue 84a [page]

1984 Mathematical Reviews  
The adherence of the set of derivations is introduced and is related to the adherence of languages.  ...  We show that the topology of derivations has a continuous image in the topology of languages associated with the grammar.  ... 

Adherences of languages

Luc Boasson, Maurice Nivat
1980 Journal of computer and system sciences (Print)  
the word adherence is very convenient to talk about the w-part of the topological closure of L which is L = L U Adh(L).  ...  BOASSON AND NIVAT is an algebraic adherence since B is the adherence of the Lukaziewicz language One can remark that B is also the adherence of the Dyck language on one letter 0; = {w E {a, b}* I j w  ... 
doi:10.1016/0022-0000(80)90010-0 fatcat:2m4gm26zjraj3hd327s26pg3nq
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