103,802 research outputs found
Efficient Algorithms for Membership in Boolean Hierarchies of Regular Languages
The purpose of this paper is to provide efficient algorithms that decide
membership for classes of several Boolean hierarchies for which efficiency (or
even decidability) were previously not known. We develop new forbidden-chain
characterizations for the single levels of these hierarchies and obtain the
following results: - The classes of the Boolean hierarchy over level
of the dot-depth hierarchy are decidable in (previously only the
decidability was known). The same remains true if predicates mod for fixed
are allowed. - If modular predicates for arbitrary are allowed, then
the classes of the Boolean hierarchy over level are decidable. - For
the restricted case of a two-letter alphabet, the classes of the Boolean
hierarchy over level of the Straubing-Th\'erien hierarchy are
decidable in . This is the first decidability result for this hierarchy. -
The membership problems for all mentioned Boolean-hierarchy classes are
logspace many-one hard for . - The membership problems for quasi-aperiodic
languages and for -quasi-aperiodic languages are logspace many-one complete
for
Width Hierarchy for k-OBDD of Small Width
In this paper was explored well known model k-OBDD. There are proven width
based hierarchy of classes of boolean functions which computed by k-OBDD. The
proof of hierarchy is based on sufficient condition of Boolean function's non
representation as k-OBDD and complexity properties of Boolean function SAF.
This function is modification of known Pointer Jumping (PJ) and Indirect
Storage Access (ISA) functions.Comment: 8 page
Symmetry in Critical Random Boolean Network Dynamics
Using Boolean networks as prototypical examples, the role of symmetry in the
dynamics of heterogeneous complex systems is explored. We show that symmetry of
the dynamics, especially in critical states, is a controlling feature that can
be used both to greatly simplify analysis and to characterize different types
of dynamics. Symmetry in Boolean networks is found by determining the frequency
at which the various Boolean output functions occur. There are classes of
functions that consist of Boolean functions that behave similarly. These
classes are orbits of the controlling symmetry group. We find that the symmetry
that controls the critical random Boolean networks is expressed through the
frequency by which output functions are utilized by nodes that remain active on
dynamical attractors. This symmetry preserves canalization, a form of network
robustness. We compare it to a different symmetry known to control the dynamics
of an evolutionary process that allows Boolean networks to organize into a
critical state. Our results demonstrate the usefulness and power of using the
symmetry of the behavior of the nodes to characterize complex network dynamics,
and introduce a novel approach to the analysis of heterogeneous complex
systems
Spectra of Tukey types of ultrafilters on Boolean algebras
Extending recent investigations on the structure of Tukey types of
ultrafilters on to Boolean algebras in general, we
classify the spectra of Tukey types of ultrafilters for several classes of
Boolean algebras, including interval algebras, tree algebras, and pseudo-tree
algebras.Comment: 18 page
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