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On injective endomorphisms of symbolic schemes [article]

Tullio Ceccherini-Silberstein, Michel Coornaert, Xuan Kien Phung
2018 arXiv   pre-print
We also establish several new ones regarding the closed image property, surjunctivity, reversibility, and invertibility for cellular automata over algebraic varieties with coefficients in an algebraically  ...  Building on the seminal work of Gromov on endomorphisms of symbolic algebraic varieties [10], we introduce a notion of cellular automata over schemes which generalize affine algebraic cellular automata  ...  As Spec(R) is quasi-compact for any ring R, we deduce that every subset of the underlying topological space of a quasi-compact scheme is quasi-compact for the induced topology.  ... 
arXiv:1712.05716v3 fatcat:az4ez3fc5zerbjksroygxtayma

Page 7774 of Mathematical Reviews Vol. , Issue 96m [page]

1996 Mathematical Reviews  
to A is a right zero decomposition of pairwise isomorphic group-type quasi- automata.  ...  The second part deals with effective approximations of uncount- able topological algebras.  ... 

Page 6637 of Mathematical Reviews Vol. , Issue 90K [page]

1990 Mathematical Reviews  
With aspects from topology.  ...  height, star height and finite automata with distance functions (pp. 74-88); John Meakin, Automata and the word problem (pp. 89- 103); Wolfgang Thomas, Automata and quantifier hierarchies (pp. 104-119)  ... 

Page 2256 of Mathematical Reviews Vol. , Issue 89D [page]

1989 Mathematical Reviews  
For the class of state-independent quasi- automata the relationship between the characteristic semigroup of the generalized power quasiautomaton and the characteristic 68 COMPUTER SCIENCE semigroup of  ...  (H-BUDT) Generalized power quasiautomata. Papers on automata and languages, VIII, 33-44, DM, 86-3, Karl Marx Univ. Econom., Budapest, 1986.  ... 

Cumulative subject index volumes 40–43

1979 Information and Control  
realtime, and linear languages, 42, 27 Q Quasi-Optimizer program performance, power of heurist- ic rules in assessment, 40, 1 Queries order two, in combinatorial filing scheme, 43, 255 Questionnaire  ...  43, 20 immediate, bus automata and, 40, 88 0L-DOL equivalence problem, decidabil- ity, 40, 301 linear, realtime pushdown store automata and, 42, 27 matrix, finite index family: incomparable with  ... 
doi:10.1016/s0019-9958(79)90069-x fatcat:prorkxke6ncuzeb52kxef5whba

Page 1989 of Mathematical Reviews Vol. 52, Issue 6 [page]

1976 Mathematical Reviews  
Topological power automata with quasi-power morphisms. Math. Systems Theory 8 (1974), no. 1, 55-59.  ...  The present work is a response to this question; the rather com- plicated system presented (which we do not describe) is called a topological power automaton with a quasi-power morphism, and some of Wallace  ... 

Page 6961 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
) algebra by means of a fairly powerful apparatus (topology, group theory, vector spaces, etc.).  ...  It is shown (by analogy with finite state automata) that the quasi-regular sets— those sets accepted by some finite memory automaton—are closed under the Kleene operations and under Boolean operations  ... 

How to Prove that a Language Is Regular or Star-Free? [chapter]

Jean-Éric Pin
2020 Lecture Notes in Computer Science  
Most books of automata theory [9, 23, 29, 45, 49] offer exercises on regular languages, including some difficult ones.  ...  Another good source of tough questions is the recent book 200 Problems in Formal Languages and Automata Theory [36] . Surprisingly, there are very few exercises related to starfree languages.  ...  By a standard result of topology, K( M ), equipped with this metric, is compact. Let now τ : M → N be a transduction.  ... 
doi:10.1007/978-3-030-40608-0_5 fatcat:mzoyw7mckzgxnhyggsxiq4bhoa

Page 473 of Mathematical Reviews Vol. , Issue 96a [page]

1996 Mathematical Reviews  
It is shown that ¥ is closed under union, intersection, product, star, inverse morphisms, nonerasing direct morphisms, and intersection with regular sets.  ...  473 closed simultaneously with respect to a right-monotone and a left-monotone well quasi-order on S. Several refinements of this statement are also given.  ... 

Subject index volumes 1–200

1999 Theoretical Computer Science  
recursion theory, 737 representations of hypergraphs, 1599 size, 1637,2762 topological space, 836 topological space with a regular or self-similar structure, 3272 structure, 3272 topological spaces  ...  systems, 1757 topological dynamics, 860, 3228 of Turing machines, 3228 toolc of -. 860 topological entropies, 1272 topological entropy, 3228 topological entropy of a TMH, 3228 systems, 1272 topological  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Algebraic and topological theory of languages

J. Rhodes, P. Weil
1995 RAIRO - Theoretical Informatics and Applications  
Another essential tool of our work reveals interesting connections with topology. Let X be a finite alphabet.  ...  Furthermore, for each k > 0, X*/{I^ U {oo}) is a monoid, and if this monoid is endowed with the discrete topology, then the projection TT^ : X* -> X* /(Ik U {oo}) is a continuous morphism.  ...  In this section we will show how a rational ideal filtration is naturally associated with =.  ... 
doi:10.1051/ita/1995290100011 fatcat:ozms5mnd2vesvhg24iwx7nkxqe

Page 416 of Mathematical Reviews Vol. 54, Issue 2 [page]

1977 Mathematical Reviews  
cases in this paper) one considers the closure 2,,, of 2 in the homeo- morphism group of D (with the compact open topology).  ...  In the paper several algebraic characterizations of semi- morphisms are given and the computability of semimorphisms by automata is studied. I.  ... 

A remark on bilinear systems and moduli spaces of instantons

Eduardo D Sontag
1987 Systems & control letters (Print)  
Explicit equations are given for the moduli space of framed instantons as a quasi-affine variety, based on the representation theory of noncommutative power series, or equivalently, the minimal realization  ...  The corresponding sequence of all possible such H α is a rational multiset or noncommutative power series, in the sense of automata theory (see [E] , [F1] , [F2] , [S1] , [S2] ).  ...  g = f • h on this open set, which is a morphism as desired. We summarize the above discussion with: Theorem 3.1. The mapping γ : B → N is a quotient of B under the action of GL(n, C). §4.  ... 
doi:10.1016/0167-6911(87)90064-8 fatcat:mlvlucvygbdj5gv2j36cnda25y

Dual Space of a Lattice as the Completion of a Pervin Space [chapter]

Jean-Éric Pin
2017 Lecture Notes in Computer Science  
We assume the reader is familiar with basic topology on the one hand and finite automata theory on the other hand. No proofs are given in this extended abstract.  ...  A natural attempt would be to mimic the definition used for topological spaces (and for quasi-uniform spaces): a quotient map ϕ : X → Y should be a surjective morphism 2 such that Y is equipped with the  ...  Pervin spaces are thus easier to define than topological spaces or (quasi)-uniform spaces.  ... 
doi:10.1007/978-3-319-57418-9_2 fatcat:blqgjzhya5gc3cmecdd2dtgoxy

Page 7351 of Mathematical Reviews Vol. , Issue 2000j [page]

2000 Mathematical Reviews  
The g power is strongly avoidable over an n-letter alphabet if there exists an infinite n-letter word not containing a commutative r power with r > g.  ...  of curves under topological deformations.  ... 
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