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### Extensions of iterative congruences on free iterative algebras

Francesco Parisi-Presicce
1983 Journal of computer and system sciences (Print)
Then Rx/K' is iterative. The notion of extension of a congruence K on R, is a natural one.  ...  It is proved that if a congruence on Ez induces an iterative factor algebra, then so does its extension on R,.  ...  ACKNOWLEDGMENT The author wishes to express his gratitude to Professor George Raney for many helpful suggestions and encouragement during the development of this research at The University of Connecticut  ...

### Iteration algebras extended abstract [chapter]

Stephen L. Bloom, Zoltán Ésik
1991 Lecture Notes in Computer Science
In any case, each congruence "~n is a dagger congruence, so that T t has all finitely generated free algebras. It follows that T? has all free algebras, by Theorem 2.1.  ...  EXAMPLE 4.3 An example of an iteration theory T such that T t has all free algebras, but T i # T ~.  ...

### Page 5434 of Mathematical Reviews Vol. , Issue 97I [page]

1997 Mathematical Reviews
In the case of solutions of algebraic equation systems a generalization of the iteration lemma for context-free languages can be shown.” 97i:20069 20M05 20M14 Rosales, J.C.  ...  A morphism (or congruence) satisfying the defini- tion is shown to have the desired extension properties; the authors give examples to show that a bimorphism (congruence) may have the extension property  ...

### Iteractive factor algebras and induced metrics

Francesco Parisi-Presicce
1983 Theoretical Computer Science
A necessary and sufficient condition for a congruence on the algebra of regular trees to induce an iterative factor algebra is presented and possible induced distance functions are discussed.  ...  An algebra is said to be iterative if every nontrivial finite system of fixed-point equations has a unique solution.  ...  Let A be an iterative Z-algebra and h : RTL-(A) + A the (unique) extension of id : ,4 + A to a Z-homomorphism. Let K = ker h.  ...

### Page 4832 of Mathematical Reviews Vol. , Issue 83m [page]

1983 Mathematical Reviews
(The free spectrum of D is defined to be the sequence (S,(D)),,>09, where S,(D) is the cardinality of the free algebra on n free generators in Var({ E,.,D)).)  ...  Let Z(V) denote the subvariety in V consisting of those algebras A in V for which the diagonal A = {(a,a):a€A} is a 0-class for a congruence 6 on A XA.  ...

### Regular trees and the free iterative theory

Susanna Ginali
1979 Journal of computer and system sciences (Print)
Any iterative theory has a "presentation" in terms of the free iterative theory 12 and a set of identities (involving trees in JJ which determine a congruence on the morphism sets of IX.  ...  More recently, an algebraic formulation and extension of the Chomsky hierarchy appeared in Wand [lq.  ...

### Unique fixed points vs. least fixed points

Jerzy Tiuryn
1980 Theoretical Computer Science
We prove that such extensions always exist, the construction of a free extension is given.  ...  The notion of an iterative algebra is introduced in this paper, and it is shown here that it corresponds to the notion of iterative algebraic theory.  ...  i;truction of free iterative theories by using the result of Ginali  relating free iterative algebras with free rational theories.  ...

### Page 5150 of Mathematical Reviews Vol. , Issue 85k [page]

1985 Mathematical Reviews
Veloso (Rio de Janeiro) Parisi-Presicce, Francesco (1-SCA) 85k:68061 Extensions of iterative congruences on free iterative algebras. J. Comput. System Sci. 27 (1983), no. 2, 200-220.  ...  The idea of the proof yields a more general result characterizing iterative factor algebras of the L-algebra of partial regular trees in terms of congruences in the L-algebra of total regular trees.  ...

### Page 1241 of Mathematical Reviews Vol. , Issue 81D [page]

1981 Mathematical Reviews
A. 81d:03061 Homomorphisms of totally bounded extensions of iterative Post algebras. (Russian) Rostock. Math. Kollog. No. 11 (1979), 85-92.  ...  The author shows that %,, the free diagonalizable algebra on a de- numerable set of generators, is a subalgebra of P. Moreover, GF €HP{P}, PEH{G,} and ?  ...

### On Free Completely Iterative Algebras

2020 Annual Conference for Computer Science Logic
Moreover, the algebra structure of the latter is the unique continuous extension of the algebra structure of the free algebra.  ...  And for every recursive equation in the free completely iterative algebra the solution is obtained as the join of an ω-chain of approximate solutions in the free algebra.  ...  completion. 7:2 On Free Completely Iterative Algebras Moreover, the coalgebra structure of νF is the unique continuous extension of the inverted algebra structure of µF .  ...

### Page 36 of American Mathematical Society. Bulletin of the American Mathematical Society Vol. 61, Issue 1 [page]

1955 American Mathematical Society. Bulletin of the American Mathematical Society
Let A be an arbitrary odd ideal of a finite extension F of the rational field. Denote by ».(o) the number of solutions of the congruence p=aXit+ tee +a,X?  ...  Fine and Bertram Kus:unt (p): The group of formal power series under iteration. The authors study the topological group, under iteration, of formal power series a:x-+-a2x?  ...

### Fregean logics with the multiterm deduction theorem and their algebraization

J. Czelakowski, D. Pigozzi
2004 Studia Logica: An International Journal for Symbolic Logic
a congruence relation on the formula algebra.  ...  Moreover, it is algebraizable and the algebraic structure of its equivalent quasivariety is very close to that of the variety of Hilbert algebras.  ...  This refers to any one of the extensions of free equational logic by additional axioms and rules of inference.  ...

### Semantics of flowchart programs and the free Conway theories

L. Bernátsky, Z. Ésik
1998 RAIRO - Theoretical Informatics and Applications
Comparing the structure of the free Conway théories with that of the free itération theory, we obtain a clear picture of that part of the equational theory of itération théories which is captured by the  ...  Thus the least congruence on S-schemes whose quotient is a theory gives the free Conway theory on S. The second main resuit, Theorem 6.1, provides an explicit description of the free Conway théories.  ...  Proof: This is an immédiate conséquence of Lemmas 6.2 and 6.3. •  ...

### Page 945 of Mathematical Reviews Vol. , Issue 84c [page]

1984 Mathematical Reviews
945 CATEGORY THEORY, HOMOLOGICAL ALGEBRA annihilate a free Mal’tsev ®-algebra from k>6 generators.  ...  Finally, new elements of the commutative center, which have minimal known degree, are obtained in a free alternative ®-algebra from k>6 generators.  ...

### Page 3593 of Mathematical Reviews Vol. , Issue 2004e [page]

2004 Mathematical Reviews
Summary: “We obtain the construction of free abelian extensions in a congruence-permutable variety 7 using the construction of a free abelian extension in a variety of algebras with one ternary Mal’cev  ...  = y and t;)(x,x) =e; for each i = 1 - 2004e:08006 08B10 08B05 08B20 Zhdanovich, Pavel Free abelian extensions in the congruence-permutable varieties.  ...
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