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1
Decision Procedures for
Equationally Based Reasoning
Each of these theoretical topics have lead to the development of new libraries and tools.
2
Algorithmic Problems in Groups and Semigroups
Then a G-group H is called G-equationally Noetherian if for every n > 0 and every
subset SofG[x\,...,xn] there exists a finite subset SQ of S such that VH(S) = VH(S0).
In the event that G = H we simply say that G is equationally Noetherian, ...
Jean-Camille Birget,
2000
2 is called equationally complete if whenever SsS', where 2' is strictly consistent,
thenTi=H'. Let us note that an equationally complete set of identities be always
closed. Definition 3. An equational class K of algebras is equationally complete ...
4
Summer School in Group Theory in Banff, 1996
I have chosen to single out only a special case of one concept here, that of an
equationally Noetherian group, introduced in [9] (see also [10]), where details of
this and other notions are defined in complete detail and generality. To this end,
let ...
5
Lattice Functions and Equations
In view of Remark 3.2.5, a bounded lattice L is {2-}equationally {mono}compact in
the class of lattices if and only if it has this property in the class of bounded
lattices. □ Theorem 2.2. The following properties are equivalent for a lattice L: (i)
L is ...
6
Group Theory, Statistics, and Cryptography
V(G, S) = {g e Gn : s(g) = 1 for all s(x) € 5} is the solution set in G to the system 5=
1. (B) The group G is equationally Noetherian provided for every integer n > 0
and every system S = 1 of equations in n variables Xn = {xi, ...,£n} there is a finite
...
7
Geometric Group Theory: Geneva and Barcelona Conferences
Then a group G is equationally noetherian if and only if for each n ≥ 1 the Zariski
topology on Gn is noetherian [2, Theorem D1]. Guba has shown that free groups
are equationally noetherian using the fact that a free group is linear [8].
Goulnara N. Arzhantseva, Laurent Bartholdi, Jose Burillo,
2007
8
Canadian Mathematical Bulletin
PROPOSITION 1. A G-set A is equationally compact iffZA = QA, i.e. any subgroup
HofGfor which every finitely generated subgroup is contained in some stability
group of A is itself contained in a stability group of A. Proof. If A is equationally ...
9
Groups St Andrews 2001 in Oxford:
Then H is G-equationally noetherian if for every integer n > 0 and every subset
S C G[xi, ...,x„] there is a finite subset SO C S such that Vn(S) = VH(SQ). G itself is
equationally noetherian provided it is G-equationally noetherian. It was shown in
...
C. M. Campbell, E. F. Robertson, G. C. Smith,
2003
10
FGCS '92: Fifth Generation Computer Systems 1992
Note that for every flat gual clause :- C. REDU( -~C) is equationally equivalent to '
--C. Theorem 3.2 [Cox et al. 1991] Lei :- C be a goal clause and A a set of Horn
clause* which includes the function substitutivity axioms. Then A equationally ...
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Master Regulator Of Chromosomal Segregation Identified
In mitosis, the replicated chromosomes (sister chromatids) are segregated equationally, with one sister chromatid moving to each spindle pole. «Asian Scientist Magazine, 3月 15»