8,955 research outputs found
The Non-Archimedean Theory of Discrete Systems
In the paper, we study behavior of discrete dynamical systems (automata)
w.r.t. transitivity; that is, speaking loosely, we consider how diverse may be
behavior of the system w.r.t. variety of word transformations performed by the
system: We call a system completely transitive if, given arbitrary pair
of finite words that have equal lengths, the system , while
evolution during (discrete) time, at a certain moment transforms into .
To every system , we put into a correspondence a family of continuous maps of a suitable non-Archimedean metric space
and show that the system is completely transitive if and only if the family
is ergodic w.r.t. the Haar measure; then we find
easy-to-verify conditions the system must satisfy to be completely transitive.
The theory can be applied to analyze behavior of straight-line computer
programs (in particular, pseudo-random number generators that are used in
cryptography and simulations) since basic CPU instructions (both numerical and
logical) can be considered as continuous maps of a (non-Archimedean) metric
space of 2-adic integers.Comment: The extended version of the talk given at MACIS-201
Describing the set of words generated by interval exchange transformation
Let be an infinite word over finite alphabet . We get combinatorial
criteria of existence of interval exchange transformations that generate the
word W.Comment: 17 pages, this paper was submitted at scientific council of MSU,
date: September 21, 200
The Sigma-Semantics: A Comprehensive Semantics for Functional Programs
A comprehensive semantics for functional programs is presented, which generalizes the well-known call-by-value and call-by-name semantics. By permitting a separate choice between call-by value and call-by-name for every argument position of every function and parameterizing the semantics by this choice we abstract from the parameter-passing mechanism. Thus common and distinguishing features of all instances of the sigma-semantics, especially call-by-value and call-by-name semantics, are highlighted. Furthermore, a property can be validated for all instances of the sigma-semantics by a single proof. This is employed for proving the equivalence of the given denotational (fixed-point based) and two operational (reduction based) definitions of the sigma-semantics. We present and apply means for very simple proofs of equivalence with the denotational sigma-semantics for a large class of reduction-based sigma-semantics. Our basis are simple first-order constructor-based functional programs with patterns
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