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A Homomorphism Concept for omega-Regularity

1994
*
BRICS Report Series
*

The Myhill-Nerode Theorem (that

doi:10.7146/brics.v1i11.21659
fatcat:cusz7iai2vaoxkpr2sbyvtqcqm
*for*any*regular*language, there is*a*canonical recognizing device) is of paramount importance*for*the computational handling of many formalisms about finite words. ... <br /> <br />*For*infinite words, no prior*concept*of*homomorphism*or structural comparison seems to have generalized the Myhill-Nerode Theorem in the sense that the*concept*is both language preserving ... Thanks to Dexter Kozen, Ludwig Staiger, and Thomas Wilke*for*discussions about !-*regular*representations. ...##
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Equational specification of partial higher-order algebras

1988
*
Theoretical Computer Science
*

Axiomatic property-oriented ("'equation-oriented"') descriptions of data structures provide

doi:10.1016/0304-3975(88)90162-4
fatcat:vczkagr7arfyjkcbamxdb2ewsy
*a*powerful*concept**for*the specification, the design, and the development of algebras, consisting of families ... However,*for*making algebraic specitkations into*a*powerful practical teal*for*software engineering purposes, their theory and ?heir methodology nas to be furtkr developed. ... P&9 PUO, s)) = put@, s), iselem(x, put(y, s)) = or(eq(x, y), iselem(x, s)) Let us consider the two terms (let*omega*stand*for*pred(zero)) tl : put(*omega*, put( succ(*omega*), put( succ( succ(*omega*)), ...##
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Algebraic notions of nontermination: Omega and divergence in idempotent semirings

2010
*
The Journal of Logic and Algebraic Programming
*

Two notions of nontermination are studied and compared in the setting of idempotent semirings: Cohen's

doi:10.1016/j.jlap.2010.07.016
fatcat:khxf6uhajraztonb4fl3m4eex4
*omega*operator and*a*divergence operator. ... It turns out that divergence yields*a*simple and natural way of modelling infinite behaviours of programs and discrete systems, whereas the*omega*operator shows some anomalies. ... on*omega*and divergence. ...##
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Fixing Zeno gaps

2011
*
Theoretical Computer Science
*

We present

doi:10.1016/j.tcs.2011.03.018
fatcat:7z5acwsi2fbrzdp5wniw724ciq
*a*construction*for**a*fixpoint that captures these phenomena in*a*precise way. The theory is presented and motivated using an example from hybrid system analysis. ... It is also admirable what wide range his scientific interests span, making him*a*Jan-of-all-trades in the very best sense.*a*b s t r*a*c t In computer science, fixpoints play*a*crucial role. ... By Definition 10.4(3) twice and Definition 10.4(2), φ(ι(*a*· b)) =*a*· b = φ(ι(*a*)) · φ(ι(b)) = φ(ι(*a*) ⊙ ι(b)). ...##
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An Algebraic Approach to Energy Problems I — *-Continuous Kleene ω-Algebras

2017
*
Acta Cybernetica
*

An extended energy function is

doi:10.14232/actacyb.23.1.2017.13
fatcat:tefpfb24m5d43jsmrtclcpwcee
*a*mapping f : [0, ∞] ⊥ → [0, ∞] ⊥ ,*for*which ⊥f = ⊥ and yf ≥ xf + y − x*for*all x ≤ y. Moreover, ∞f = ∞, unless xf = ⊥*for*all x ∈ [0, ∞] ⊥ . ... This means, in particular, that xf = ⊥ implies yf = ⊥*for*all y ≤ x, and xf = ∞ implies yf = ∞*for*all y ≥ x. Hence, except*for*the extension to ∞, these ... The*omega*operation is defined as*for*languages: x ω = n≥0 x n with x n = x*for*all n ≥ 0. ...##
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Omega-Rational Expressions with Bounded Synchronization Delay

2013
*
Theory of Computing Systems
*

In this paper, we present

doi:10.1007/s00224-013-9526-4
fatcat:6o425yokf5fgjkgm6newmx62ha
*a*generalization of SD = AP to infinite words. This became possible via*a*substantial simplification of the proof*for*the corresponding result*for*finite words. ... Acknowledgements We would like to thank Jean-Éric Pin*for*bringing the class SD to our attention and*for*the proposal that the notion of local divisor might lead to*a*simplified proof*for*SD(*A** ) = AP ... (*A** ). ...##
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$\omega$-semigroups

1974
*
Rocky Mountain Journal of Mathematics
*

The

doi:10.1216/rmj-1974-4-4-597
fatcat:yolu46v7tvhg7fccomqrx74jxi
*concept*of an co-semigroup is*a*recursive analogue of*a*semigroup and is*a*generalization of an co-group. ... Finally section §7 gives*a*brief introduction to the cohomomorphism theory of co-semigroups. The author wishes to thank the referee*for*his helpful suggestions. §2. Basic*concepts*and notations. ... /i)> P2(*2> Î/2)],'*for*x 1? t/x G <*x and x 2 , t/ 2 G*a*2 . ...##
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Diagram Chase in Relational System Development

2005
*
Electronical Notes in Theoretical Computer Science
*

Diagrams are endowed with

doi:10.1016/j.entcs.2004.08.049
fatcat:gwar6lxgabhinar2m2yq3zgmla
*a*simple algebraic semantics that imposes*a*convenient balance between expressive and algorithmic power. ... We propose diagrammatic techniques*for*visualizing relational reasoning in formal methods like B or Z; in particular*for*induction and coinduction. ... Acknowledgment: The authors would like to thank the anonymous referees and the participants of the VLFM'04*for*valuable discussions. ...##
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Is Ramsey's theorem omega-automatic?
[article]

2010
*
arXiv
*
pre-print

More specifically, we show that every uncountable

arXiv:0912.2625v2
fatcat:cjzx5famsjezlorkhqeq4wkg2u
*omega*-automatic graph contains an uncountable co-context-free clique or anticlique, but not necessarily*a*context-free (let alone*regular*) clique or anticlique ... It turns out that the situation is much nicer than in general uncountable graphs, but not as nice as*for*automatic graphs. ... by*a*synchronous two-tape automaton (this*concept*is known since the beginning of automata theory,*a*systematic study started with [KN95, BG04] , see [Rub08]*for**a*recent overview). ...##
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QUASI-PROJECTIVE MODULES, PERFECT MODULES, AND A THEOREM FOR MODULAR LATTICES

1966
*
Journal of Faculty of Science Hokkaido University Series I Mathematics
*

Then, by assumption we
can easily obtain $\

doi:10.14492/hokmj/1530518491
fatcat:acqiexddi5dxlbqbco3pjcgzk4
*omega*$ in $K$ such that $(*A*\cap B)\*omega*^{-}\equiv(*A*\cap B)$ and $(x+(*A*\cap B))\overline{\*omega*}=$ $x\*omega*+(*A*\cap B)(x\in M)$ . ... Since*a**regular*ring is semi-simple, it suffices to prove that $K/J$ is*a**regular*ring. Take any element $\gamma$ of $K$ not contained in $J$ , and let $*A*$ be*a*d-complement of Mr. ...##
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The Join Levels of the Trotter-Weil Hierarchy are Decidable
[article]

2012
*
arXiv
*
pre-print

In this paper, we give

arXiv:1204.4672v1
fatcat:hs7ye5wirrerbgisvyhrissjau
*a*single identity of*omega*-terms*for*every join level of the Trotter-Weil hierarchy; this yields decidability. ... Trotter and Weil showed that*for*every band variety V there exists*a*unique maximal variety W inside DA such that the intersection with bands yields the given band variety V. ... Let u and v be two*omega*-terms over Σ.*A*finite monoid M satisfies the identity u = v if*for*every*homomorphism*ϕ : Σ * → M we have ϕ(u) = ϕ(v). ...##
###
Page 579 of Mathematical Reviews Vol. 42, Issue 3
[page]

1971
*
Mathematical Reviews
*

*A*semigroup S is said to be biregular if every principal (two-sided) ideal of S is generated by an idempotent element in the center of S. (The

*concept*of biregularity

*for*rings was introduced by R. ... The author proves that the following three conditions on

*a*semigroup S are equivalent: (1) 8 is

*a*

*regular*duo semigroup; (2) LA Q=LQ

*for*every left ideal LZ and every quasi-ideal bs of S; (3) 8 is

*a*semi ...

##
###
The Join Levels of the Trotter-Weil Hierarchy Are Decidable
[chapter]

2012
*
Lecture Notes in Computer Science
*

In this paper, we give

doi:10.1007/978-3-642-32589-2_53
fatcat:r66jpincjfg4bpzvxf5isjmx5i
*a*single identity of*omega*-terms*for*every join level of the Trotter-Weil hierarchy; this yields decidability. ... Trotter and Weil showed that*for*every band variety V there exists*a*unique maximal variety W inside DA such that the intersection with bands yields the given band variety V. ... Let u and v be two*omega*-terms over Σ.*A*finite monoid M satisfies the identity u = v if*for*every*homomorphism*ϕ : Σ * → M we have ϕ(u) = ϕ(v). ...##
###
Page 8168 of Mathematical Reviews Vol. , Issue 2004j
[page]

2004
*
Mathematical Reviews
*

Summary: “Given

*a*positive integer n and*a*finite alphabet 4,*a*word w over*A*is said to guarantee minimal image if,*for*every*homomorphism*gy from the free monoid*A** over*A*into the monoid of all transformations ... The paper is*a*continuation of the author’s works on topologi- cal properties of*omega*context free languages (@-CFL). ...##
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Two statements about infinite products that are not quite true
[article]

2005
*
arXiv
*
pre-print

(ii) There exist nontrivial rings R

arXiv:math/0508222v1
fatcat:egb2te2fmbdeznfx3iouf5tk2e
*for*which one has surjective*homomorphisms*R^\*omega*-> \bigoplus_\*omega*R -- but in such cases, R must have DCC on finitely generated right ideals. ... remaining two statements are in the context of general algebra (a.k.a. universal algebra): (i) There exist nontrivial rings R*for*which one has surjective*homomorphisms*\bigoplus_\*omega*R -> R^\*omega*- ...*A*cannot be left but not right*regular*. ...
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