Problematic Cellular Automata Segmentation and Clusterization of a Region’s Geoinformation Space

We consider the problems of clustering and segmentation for objects in the geoinformation space using the cellular automata theory, both classical and non-orthogonal ones. We clarify the terminology associated with the use of hybrid software and hardware for processing information coming from sources of different physical nature. This research is based on the geometric clusterization methods of multidimensional real or virtual spaces. As illustrative examples we consider two and three-dimensional variants, which, from our point of view, does not reduce the results’ significance in relation to the space of a greater dimension. Based on the formation conditions of the geoinformation space model as a semantic system, the use of semantic interoperability of its properties and corresponding subspaces is justified. It is shown that the unified geographic information space (UGIS) can be the data source for the formation procedures of various problem-oriented clusters used to manage socio-economic objects. As a variant of the UGIS formed subspaces this study uses a digital plan-diagram that has proven its effectiveness during previous works on the analysis of territories during their space monitoring. We also pay attention to the use of fuzzy methods and models in the processing of fuzzy source data and the clusters formation. Specific examples of clustering and segmentation using classical and non-orthogonal cellular automata are given.

Separation for dot-depth two

The dot-depth hierarchy of Brzozowski and Cohen classifies the star-free languages of finite words. By a theorem of McNaughton and Papert, these are also the first-order definable languages. The dot-depth rose to prominence following the work of Thomas, who proved an exact correspondence with the quantifier alternation hierarchy of first-order logic: each level in the dot-depth hierarchy consists of all languages that can be defined with a prescribed number of quantifier blocks. One of the most famous open problems in automata theory is to settle whether the membership problem is decidable for each level: is it possible to decide whether an input regular language belongs to this level? Despite a significant research effort, membership by itself has only been solved for low levels. A recent breakthrough was achieved by replacing membership with a more general problem: separation. Given two input languages, one has to decide whether there exists a third language in the investigated level containing the first language and disjoint from the second. The motivation is that: (1) while more difficult, separation is more rewarding (2) it provides a more convenient framework (3) all recent membership algorithms are reductions to separation for lower levels. We present a separation algorithm for dot-depth two. While this is our most prominent application, our result is more general. We consider a family of hierarchies that includes the dot-depth: concatenation hierarchies. They are built via a generic construction process. One first chooses an initial class, the basis, which is the lowest level in the hierarchy. Further levels are built by applying generic operations. Our main theorem states that for any concatenation hierarchy whose basis is finite, separation is decidable for level one. In the special case of the dot-depth, this can be lifted to level two using previously known results.

Desain Game Edukasi Ilmu Tajwid Bagi Anak Usia Dini menggunakan Pemodelan Finite State Automata

This study discusses how Finite State Automata (FSA) can be used as a model to design a Tajweed Science game application as a business diagram. This study aims to facilitate early childhood in learning the science of recitation by grouping hijaiyah letters into grouping the science of recitation by using a touch of the hand. The type of automata theory used is a non-deterministic finite automata with epsilon transition (E) or better known as E-NFA. Each transition, input, state that exists from the NFA, is basically to show the characteristics or states that occur in a game application. The importance of this research, in addition to learning recitation from an early age, is to show that automata theory can be used to help design a system in making game applications. The results of this Tajweed Science game application design are a rough display because there will still be further development stages and can ensure that game applications can be built from E-NFA modeling.

Noncommutative rational Pólya series

A (noncommutative) Pólya series over a field K is a formal power series whose nonzero coefficients are contained in a finitely generated subgroup of $$K^\times $$ K × . We show that rational Pólya series are unambiguous rational series, proving a 40 year old conjecture of Reutenauer. The proof combines methods from noncommutative algebra, automata theory, and number theory (specifically, unit equations). As a corollary, a rational series is a Pólya series if and only if it is Hadamard sub-invertible. Phrased differently, we show that every weighted finite automaton taking values in a finitely generated subgroup of a field (and zero) is equivalent to an unambiguous weighted finite automaton.

Finite State Automata-Based Representation of Device States for Function Modeling of Multi-Modal Devices

Graph-based function models used in early-stage systems design usually represent only one operational mode of the system. Currently there is a need but no rigorous formalism to model multiple possible modes and states of a device in the same model and to perform model-based reasoning with that information such as predicting state transitions or causal propagations. This paper presents a formal representation of operational modes and states of technical devices based on automata theory for both discrete and continuous state transitions. It then presents formal definitions of three signal-processing verbs that actuate or regulate energy flows: Actuate_E, Regulate_E_Discrete, and Regulate_E_Continuous. The graphical templates, definitions, grammar rules, and application of each verb in modeling is illustrated. Finally, the representation is validated by implementing it on a graphical function modeling tool and using it to illustrate the verbs' modeling and reasoning ability for predicting mode and state transitions in response to control signals and cause-and-effect propagation throughout system-level models.

Hangman–Hangaroo Game Design Using Automata Theory

Automata theory plays an important role in various areas especially in game design. This paper describes the concept of automata theory in designing one of the most popular classical game which is Hangman. In this study, we focused on a game called Hangaroo, which implemented the same concept as in Hangman game. We studied and discussed the combination of automata and game theory that can be considered in order to design the game. As a result, we found that, automata theory is the fundamental access in designing and developing Games.