Multi-island finite automata and their even computation

summary:This paper discusses $n$-island finite automata whose transition graphs can be expressed as $n$-member sequences of islands $i_1, i_2, \dots , i_n$, where there is a bridge leaving $i_j$ and entering $i_{j+1}$ for each $1 \leq j \leq n - 1$. It concentrates its attention on even computation defined as any sequence of moves during which these automata make the same number of moves in each of the islands. Under the assumption that these automata work only in an evenly computational way, the paper proves its main result stating that $n$-island finite automata and Rosebrugh-Wood $n$-parallel right-linear grammars are equivalent. Then, making use of this main result, it demonstrates that under this assumption, the language family defined by $n$-island finite automata is properly contained in that defined by $(n+1)$-island finite automata for all $n \geq 1$. The paper also points out that this infinite hierarchy occurs between the family of regular languages and that of context-sensitive languages. Open questions are formulated in the conclusion

Pattern overlap implies runaway growth in hierarchical tile systems

We show that in the hierarchical tile assembly model, if there is a producible assembly that overlaps a nontrivial translation of itself consistently (i.e., the pattern of tile types in the overlap region is identical in both translations), then arbitrarily large assemblies are producible. The significance of this result is that tile systems intended to controllably produce finite structures must avoid pattern repetition in their producible assemblies that would lead to such overlap. This answers an open question of Chen and Doty (SODA 2012), who showed that so-called "partial-order" systems producing a unique finite assembly *and" avoiding such overlaps must require time linear in the assembly diameter. An application of our main result is that any system producing a unique finite assembly is automatically guaranteed to avoid such overlaps, simplifying the hypothesis of Chen and Doty's main theorem

Human Activity Recognition through Weighted Finite Automata

ABSTRACT: This work addresses the problem of human activity identification in an ubiquitous environment, where data is collected from a wide variety of sources. In our approach, after filtering noisy sensor entries, we learn user?s behavioral patterns and activities? sensor patterns through the construction of weighted finite automata and regular expressions respectively, and infer the inhabitant?s position for each activity through frequency distribution of floor sensor data. Finally, we analyze the prediction results of this strategy, which obtains 90.65% accuracy for the test data.+This research was funded by Ministerio de Ciencia e Innovación (MICINN), Spain grant number MTM2014-55262-P and by Sociedad para el Desarrollo Regional de Cantabria (SODERCAN) grant number TI16IN-007

Concepts and analogies in cybernetics: Mathematical investigations of the role of analogy in concept formation and problem solving; with emphasis for conflict resolution via object and morphism eliminations

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.We address two problematic areas of cybernetics; nam. Analogical Problem Solving (APS) and Analogical Learning (AL). Both these human faculties do unquestionably require Intelligence. In addition, we point out that shifting of representations is the main unified theme underlying these two intellectual tasks. We focus our attention on the formulation and clarification of the notion of analogy, which has been loosely treated and used in the literature; and also on its role in shifting of representations. We describe analogizing situations in a new representational scheme, borrowed from mathematics and modified and extended to cater for our targets. We call it k-structure, closely resembling semantic networks and directed graphs; the main components of it are the so-called objects and morphisms. We argue and substantiate the need for such a representation scheme, by analysing what its constituents stand for and by cataloguing its virtues, the main one being its visual appeal and its mathematical clarity, and by listing its disadvantages when it is compared to other representation systems. Emphasis is also given to its descriptive power and usefulness by implementing it in a number of APS and AL situations. Besides representation issues, attention is paid to intelligence mechanisms which are involved in APS and AL. A cornerstone in APS and a fundamental theme in AL is the 'skeletization of k-structures'. APS is conceived as 'harmonization of skeletons'. The methodology we develop involves techniques which are computer implemented and extensively studied in theoretic terms via a proposed theory for extended k-structures. To name but a few: 1. 'the separation of the context of a concept from the concept itself', based on the ideas of k-opens and k-spaces; 2, 'object and morphism elimination' of a controversial nature; and 3. 'conflict or deadlock or dilemma resolution' which naturally arises in a k-structure interaction. The overall system, is then applied to capture the essence of EVANS' (1963) analogy-type problems and WINSTOM (1970) learning-type situations. In our attempt not to be too informal, we use basic notions and terminology from abstract Algebra, Topology and Category theory. We rather tend to be "non-logical" (analogical) in EVANS' and WINSTON's sense; "non-numeric", in MESAROVIC (1970) terms (we rather deal with abstract conceptual entities); "non-linguistic" (we do not touch natural language); and "non-resolution" oriented, in the sense of BLEDSOE (1977). However, we give hints sometimes about logical deductive axiomatic systems, employing First Order Predicate Calculus (FOPC); and about semiotics, by which we denote syntactic-semantic-pragmatic features of our system and issues of the problem domains it is acting upon. We believe in what we call: shift from the traditional 'Heuristic search paradigm' era to the 'Analogy-paradigm' era underlying Artificial Intelligence and Cybernetics. We justify this merely by listing a number of A. I. works, which employ, in some way or another, the concept of analogy, over the last fifteen years or so, where a noticeable peak is obvious during the last years and especially in 1977. Finally, we hope that if the proposed conceptual framework and techniques developed do not straightforwardly constitute some kind of platform for Artificial Intelligence, at least it would give some insights into and illuminate our understanding of the two most fundamental faculties the human brain is occupied with; namely problem solving and learning

Subshifts with Simple Cellular Automata

A subshift is a set of infinite one- or two-way sequences over a fixed finite set, defined by a set of forbidden patterns. In this thesis, we study subshifts in the topological setting, where the natural morphisms between them are ones defined by a (spatially uniform) local rule. Endomorphisms of subshifts are called cellular automata, and we call the set of cellular automata on a subshift its endomorphism monoid. It is known that the set of all sequences (the full shift) allows cellular automata with complex dynamical and computational properties. We are interested in subshifts that do not support such cellular automata. In particular, we study countable subshifts, minimal subshifts and subshifts with additional universal algebraic structure that cellular automata need to respect, and investigate certain criteria of ‘simplicity’ of the endomorphism monoid, for each of them. In the case of countable subshifts, we concentrate on countable sofic shifts, that is, countable subshifts defined by a finite state automaton. We develop some general tools for studying cellular automata on such subshifts, and show that nilpotency and periodicity of cellular automata are decidable properties, and positive expansivity is impossible. Nevertheless, we also prove various undecidability results, by simulating counter machines with cellular automata. We prove that minimal subshifts generated by primitive Pisot substitutions only support virtually cyclic automorphism groups, and give an example of a Toeplitz subshift whose automorphism group is not finitely generated. In the algebraic setting, we study the centralizers of CA, and group and lattice homomorphic CA. In particular, we obtain results about centralizers of symbol permutations and bipermutive CA, and their connections with group structures.Siirretty Doriast

Processing hidden Markov models using recurrent neural networks for biological applications

Philosophiae Doctor - PhDIn this thesis, we present a novel hybrid architecture by combining the most popular sequence recognition models such as Recurrent Neural Networks (RNNs) and Hidden Markov Models (HMMs). Though sequence recognition problems could be potentially modelled through well trained HMMs, they could not provide a reasonable solution to the complicated recognition problems. In contrast, the ability of RNNs to recognize the complex sequence recognition problems is known to be exceptionally good. It should be noted that in the past, methods for applying HMMs into RNNs have been developed by other researchers. However, to the best of our knowledge, no algorithm for processing HMMs through learning has been given. Taking advantage of the structural similarities of the architectural dynamics of the RNNs and HMMs, in this work we analyze the combination of these two systems into the hybrid architecture. To this end, the main objective of this study is to improve the sequence recognition/classi_cation performance by applying a hybrid neural/symbolic approach. In particular, trained HMMs are used as the initial symbolic domain theory and directly encoded into appropriate RNN architecture, meaning that the prior knowledge is processed through the training of RNNs. Proposed algorithm is then implemented on sample test beds and other real time biological applications