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The existence and uniqueness (up to equivalence defined below) of code loops was first established by R. Griess in [3]. Nevertheless, the explicit construction of code loops remained open until T. Hsu introduced the notion of symplectic cubic spaces and their Frattini extensions, and pointed out how the construction of code loops followed from the (purely combinatorial) result of O. Chein and E. Goodaire contained in [2]. Within this paper, we focus on their combinatorial construction and prove...
A compatibility relation on letters induces a reflexive and
symmetric relation on words of equal length. We consider these word
relations with respect to the theory of variable length codes and
free monoids. We define an (R,S)-code and an (R,S)-free monoid
for arbitrary word relations R and S. Modified
Sardinas-Patterson algorithm is presented for testing whether finite
sets of words are (R,S)-codes. Coding capabilities of relational
codes are measured algorithmically by finding minimal and maximal
relations....
Branching programs are a well-established computation model for boolean functions, especially read-once branching programs (BP1s) have been studied intensively. Recently two restricted nondeterministic (parity) BP1 models, called nondeterministic (parity) graph-driven BP1s and well-structured nondeterministic (parity) graph-driven BP1s, have been investigated. The consistency test for a BP-model is the test whether a given BP is really a BP of model . Here it is proved that the consistency test...
Branching programs are a well-established computation model for boolean functions,
especially read-once branching programs (BP1s) have been studied intensively.
Recently two restricted nondeterministic (parity)
BP1 models,
called nondeterministic (parity) graph-driven BP1s and well-structured
nondeterministic (parity) graph-driven BP1s,
have been investigated. The consistency test for a BP-model M is the test
whether a given BP is really a BP of model M.
Here it is proved that the consistency...
We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. This method, together with the solution of the conjugacy problem given by the authors in [9], are two main steps for solving conjugacy systems, thus breaking recently discovered cryptosystems based in braid groups [2]. We also present the result of our computations, where we notice that our algorithm yields surprisingly small generating sets for the centralizers.
To the two classical reversible 1-bit logic gates, i.e. the identity
gate (a.k.a. the follower) and the NOT gate (a.k.a. the inverter), we add an
extra gate, the square root of NOT. Similarly, we add to the 24 classical reversible 2-bit circuits, both the square root of NOT and the controlled square
root of NOT. This leads to a new kind of calculus, situated between classical
reversible computing and quantum computing.
The investigations of conditional distributivity are encouraged by distributive logical connectives and their generalizations used in fuzzy set theory and were brought into focus by Klement in the closing session of Linzs 2000. This paper is mainly devoted to characterizing all pairs of aggregation functions that are satisfying conditional distributivity laws, where is an overlap function, and is a continuous t-conorm or a uninorm with continuous underlying operators.
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