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A Homomorphism Concept for omega-Regularity

Nils Klarlund
1994 BRICS Report Series  
The Myhill-Nerode Theorem (that 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.  ... 
doi:10.7146/brics.v1i11.21659 fatcat:cusz7iai2vaoxkpr2sbyvtqcqm

Equational specification of partial higher-order algebras

Manfred Broy
1988 Theoretical Computer Science  
Axiomatic property-oriented ("'equation-oriented"') descriptions of data structures provide 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)),  ... 
doi:10.1016/0304-3975(88)90162-4 fatcat:vczkagr7arfyjkcbamxdb2ewsy

Algebraic notions of nontermination: Omega and divergence in idempotent semirings

Peter Höfner, Georg Struth
2010 The Journal of Logic and Algebraic Programming  
Two notions of nontermination are studied and compared in the setting of idempotent semirings: Cohen's 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.  ... 
doi:10.1016/j.jlap.2010.07.016 fatcat:khxf6uhajraztonb4fl3m4eex4

Fixing Zeno gaps

Peter Höfner, Bernhard Möller
2011 Theoretical Computer Science  
We present 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)).  ... 
doi:10.1016/j.tcs.2011.03.018 fatcat:7z5acwsi2fbrzdp5wniw724ciq

An Algebraic Approach to Energy Problems I — *-Continuous Kleene ω-Algebras

Zoltán Ésik, Uli Fahrenberg, Axel Legay, Karin Quaas
2017 Acta Cybernetica  
An extended energy function is 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.  ... 
doi:10.14232/actacyb.23.1.2017.13 fatcat:tefpfb24m5d43jsmrtclcpwcee

Omega-Rational Expressions with Bounded Synchronization Delay

Volker Diekert, Manfred Kufleitner
2013 Theory of Computing Systems  
In this paper, we present 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 * ).  ... 
doi:10.1007/s00224-013-9526-4 fatcat:6o425yokf5fgjkgm6newmx62ha

$\omega$-semigroups

C.H. Applebaum
1974 Rocky Mountain Journal of Mathematics  
The 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 .  ... 
doi:10.1216/rmj-1974-4-4-597 fatcat:yolu46v7tvhg7fccomqrx74jxi

Diagram Chase in Relational System Development

Michael Ebert, Georg Struth
2005 Electronical Notes in Theoretical Computer Science  
Diagrams are endowed with 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.  ... 
doi:10.1016/j.entcs.2004.08.049 fatcat:gwar6lxgabhinar2m2yq3zgmla

Is Ramsey's theorem omega-automatic? [article]

Dietrich Kuske
2010 arXiv   pre-print
More specifically, we show that every uncountable 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).  ... 
arXiv:0912.2625v2 fatcat:cjzx5famsjezlorkhqeq4wkg2u

QUASI-PROJECTIVE MODULES, PERFECT MODULES, AND A THEOREM FOR MODULAR LATTICES

Yôichi Miyashita
1966 Journal of Faculty of Science Hokkaido University Series I Mathematics  
Then, by assumption we can easily obtain $\omega$ 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.  ... 
doi:10.14492/hokmj/1530518491 fatcat:acqiexddi5dxlbqbco3pjcgzk4

The Join Levels of the Trotter-Weil Hierarchy are Decidable [article]

Manfred Kufleitner, Alexander Lauser
2012 arXiv   pre-print
In this paper, we give 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).  ... 
arXiv:1204.4672v1 fatcat:hs7ye5wirrerbgisvyhrissjau

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]

Manfred Kufleitner, Alexander Lauser
2012 Lecture Notes in Computer Science  
In this paper, we give 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).  ... 
doi:10.1007/978-3-642-32589-2_53 fatcat:r66jpincjfg4bpzvxf5isjmx5i

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).  ... 

Two statements about infinite products that are not quite true [article]

George M. Bergman
2005 arXiv   pre-print
(ii) There exist nontrivial rings R 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.  ... 
arXiv:math/0508222v1 fatcat:egb2te2fmbdeznfx3iouf5tk2e
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