-catégories and gamuts
-valuations of graphs
Baire classification and infinite perceptrons
Balanced problems on graphs with categorization of edges
Suppose a graph G = (V,E) with edge weights w(e) and edges partitioned into disjoint categories S₁,...,Sₚ is given. We consider optimization problems on G defined by a family of feasible sets (G) and the following objective function: For an arbitrary number of categories we show that the L₅-perfect matching, L₅-a-b path, L₅-spanning tree problems and L₅-Hamilton cycle (on a Halin graph) problem are NP-complete. We also summarize polynomiality results concerning above objective functions for arbitrary...
Batch scheduling problem with due-date and fuzzy precedence relation
A single-machine batch scheduling problem is investigated. Each job has a positive processing time and due-date. Setup times are assumed to be identical for all batches. All batch sizes cannot exceed a common upper bound. As in many practical situations, jobs have to be subject to flexible precedence constraints. The aim of this paper is to find an optimal batch sequence. The sequence is to minimize the maximal completion time and maximize the minimum value of desirability of the fuzzy precedence....
Behaviour of finite automata in infinite environment [Abstract of thesis]
Berkowitz's algorithm and clow sequences.
Bias-variance decomposition in Genetic Programming
We study properties of Linear Genetic Programming (LGP) through several regression and classification benchmarks. In each problem, we decompose the results into bias and variance components, and explore the effect of varying certain key parameters on the overall error and its decomposed contributions. These parameters are the maximum program size, the initial population, and the function set used. We confirm and quantify several insights into the practical usage of GP, most notably that (a) the...
Bicolored digraph grammar systems
Bidirectional string assembling systems
We introduce and investigate several variants of a bidirectional string assembling system, which is a computational model that generates strings from copies of assembly units. The underlying mechanism is based on two-sided piecewise assembly of a double-stranded sequence of symbols, where the upper and lower strand have to match. The generative capacities and the relative power of the variants are our main interest. In particular, we prove that bidirectional string assembling system generate languages...
Bi-infinitary codes
Bijective sequential mappings of a free monoid onto another
Binary operations on automatic functions
Real functions on the domain – often used to describe digital images – allow for different well-known types of binary operations. In this note, we recapitulate how weighted finite automata can be used in order to represent those functions and how certain binary operations are reflected in the theory of these automata. Different types of products of automata are employed, including the seldomly-used full cartesian product. We show, however, the infeasibility of functional composition; simple examples...
Binary operations on automatic functions
Real functions on the domain [0,1)n – often used to describe digital images – allow for different well-known types of binary operations. In this note, we recapitulate how weighted finite automata can be used in order to represent those functions and how certain binary operations are reflected in the theory of these automata. Different types of products of automata are employed, including the seldomly-used full Cartesian product. We show, however, the infeasibility of functional composition; simple...
Binary patterns in binary cube-free words: Avoidability and growth
The avoidability of binary patterns by binary cube-free words is investigated and the exact bound between unavoidable and avoidable patterns is found. All avoidable patterns are shown to be D0L-avoidable. For avoidable patterns, the growth rates of the avoiding languages are studied. All such languages, except for the overlap-free language, are proved to have exponential growth. The exact growth rates of languages avoiding minimal avoidable patterns are approximated through computer-assisted upper...
Biomolecular nonlinear dynamic mechanisms as a foundation for human traits of information processing machine.
Bipolar fuzzy finite state machines.
Bisimulation on speed : lower time bounds
More than a decade ago, Moller and Tofts published their seminal work on relating processes, which are annotated with lower time bounds, with respect to speed. Their paper has left open many questions regarding the semantic theory for the suggested bisimulation-based faster-than preorder, the MT-preorder, which have not been addressed since. The encountered difficulties concern a general compositionality result, a complete axiom system for finite processes, a convincing intuitive justification of...
Bisimulation on speed: Lower time bounds
More than a decade ago, Moller and Tofts published their seminal work on relating processes, which are annotated with lower time bounds, with respect to speed. Their paper has left open many questions regarding the semantic theory for the suggested bisimulation-based faster-than preorder, the MT-preorder, which have not been addressed since. The encountered difficulties concern a general compositionality result, a complete axiom system for finite processes, a convincing intuitive justification...
Block decomposition approach to compute a minimum geodetic set
In this paper, we develop a divide-and-conquer approach, called block decomposition, to solve the minimum geodetic set problem. This provides us with a unified approach for all graphs admitting blocks for which the problem of finding a minimum geodetic set containing a given set of vertices (g-extension problem) can be efficiently solved. Our method allows us to derive linear time algorithms for the minimum geodetic set problem in (a proper superclass of) block-cacti and monopolar chordal graphs....