Search results for "rete"

A Generalization of Girod’s Bidirectional Decoding Method to Codes with a Finite Deciphering Delay

2012

In this paper we generalize an encoding method due to Girod (cf. [6]) using prefix codes, that allows a bidirectional decoding of the encoded messages. In particular we generalize it to any finite alphabet A, to any operation defined on A, to any code with finite deciphering delay and to any key x ∈ A+ , on a length depending on the deciphering delay. We moreover define, as in [4], a deterministic transducer for such generalized method. We prove that, fixed a code X ∈ A* with finite deciphering delay and a key x ∈ A *, the transducers associated to different operations are isomorphic as unlabelled graphs. We also prove that, for a fixed code X with finite deciphering delay, transducers asso…

DEFECT THEOREMS FOR TREES

2000

We generalize different notions of a rank of a set of words to sets of trees. We prove that almost all of those ranks can be used to formulate a defect theorem. However, as we show, the prefix rank forms an exception.

Weak regularity and consecutive topologizations and regularizations of pretopologies

2009

Abstract L. Foged proved that a weakly regular topology on a countable set is regular. In terms of convergence theory, this means that the topological reflection Tξ of a regular pretopology ξ on a countable set is regular. It is proved that this still holds if ξ is a regular σ -compact pretopology. On the other hand, it is proved that for each n ω there is a (regular) pretopology ρ (on a set of cardinality c ) such that ( RT ) k ρ > ( RT ) n ρ for each k n and ( RT ) n ρ is a Hausdorff compact topology, where R is the reflector to regular pretopologies. It is also shown that there exists a regular pretopology of Hausdorff RT -order ⩾ ω 0 . Moreover, all these pretopologies have the property…

Groups whose prime graph on conjugacy class sizes has few complete vertices

2012

Abstract Let G be a finite group, and let Γ ( G ) denote the prime graph built on the set of conjugacy class sizes of G. In this paper, we consider the situation when Γ ( G ) has “few complete vertices”, and our aim is to investigate the influence of this property on the group structure of G. More precisely, assuming that there exists at most one vertex of Γ ( G ) that is adjacent to all the other vertices, we show that G is solvable with Fitting height at most 3 (the bound being the best possible). Moreover, if Γ ( G ) has no complete vertices, then G is a semidirect product of two abelian groups having coprime orders. Finally, we completely characterize the case when Γ ( G ) is a regular …

Quantum Finite Multitape Automata

1999

Quantum finite automata were introduced by C. Moore, J. P. Crutchfield [4], and by A. Kondacs and J. Watrous [3]. This notion is not a generalization of the deterministic finite automata. Moreover, in [3] it was proved that not all regular languages can be recognized by quantum finite automata. A. Ambainis and R. Freivalds [1] proved that for some languages quantum finite automata may be exponentially more concise rather than both deterministic and probabilistic finite automata. In this paper we introduce the notion of quantum finite multitape automata and prove that there is a language recognized by a quantum finite automaton but not by deterministic or probabilistic finite automata. This …

Probabilistic Reversible Automata and Quantum Automata

2002

To study relationship between quantum finite automata and probabilistic finite automata, we introduce a notion of probabilistic reversible automata (PRA, or doubly stochastic automata). We find that there is a strong relationship between different possible models of PRA and corresponding models of quantum finite automata. We also propose a classification of reversible finite 1-way automata.

Implications of quantum automata for contextuality

2014

We construct zero error quantum finite automata (QFAs) for promise problems which cannot be solved by bounded error probabilistic finite automata (PFAs). Here is a summary of our results: There is a promise problem solvable by an exact two way QFA in exponential expected time but not by any bounded error sublogarithmic space probabilistic Turing machine (PTM). There is a promise problem solvable by an exact two way QFA in quadratic expected time but not by any bounded error o(loglogn) space PTMs in polynomial expected time. The same problem can be solvable by a one way Las Vegas (or exact two way) QFA with quantum head in linear (expected) time. There is a promise problem solvable by a Las …

Amount of Nonconstructivity in Finite Automata

2009

When D. Hilbert used nonconstructive methods in his famous paper on invariants (1888), P.Gordan tried to prevent the publication of this paper considering these methods as non-mathematical. L. E. J. Brouwer in the early twentieth century initiated intuitionist movement in mathematics. His slogan was "nonconstructive arguments have no value for mathematics". However, P. Erdos got many exciting results in discrete mathematics by nonconstructive methods. It is widely believed that these results either cannot be proved by constructive methods or the proofs would have been prohibitively complicated. R.Freivalds [7] showed that nonconstructive methods in coding theory are related to the notion of…

Every Quojection is the Quotient of a Countable Product of Banach Spaces

1989

It is proved that every quojection in the sense of Bellenot and Dubinsky [1] is the quotient of a countable product of copies of l 1 (I) for a suitable index set I.

A Uniform Way to Control Chief Series in Finite p -Groups and to Construct the Countable Algebraically Closed Locally Finite p -Groups

1986