Probabilistic Automata Research Articles

A Formal Model for Semantic Computing Based on Generalized Probabilistic Automata

In most previous research, “semantic computing” refers to computational implementations of semantic reasoning. It lacks support from the formal theory of computation. To provide solid foundations for semantic computing, researchers propose a different understanding of semantic computing based on finite automata. This approach provides a computer theoretical approach to semantic computing. But finite automata are not capable enough to deal with imprecise knowledge. Therefore, in this paper, we provide foundations for semantic computing based on probabilistic automata. Even though traditional probabilistic automata can handle imprecise knowledge, their limitation resides in their being defined on a fixed finite input alphabet. This deeply restricts the abilities of automata. In this paper, we rebuild traditional probabilistic automata for semantic computing. Furthermore, our new probabilistic automata are robust enough to handle any alphabet as input. They have better performances in many applications. We provide an application for weather forecasting, a domain for which traditional probabilistic automata are not effective due to their finite input alphabet. Our new probabilistic automata can overcome these limitations.

Freeness properties of weighted and probabilistic automata over bounded languages

There has been much research into freeness properties of finitely generated matrix semigroups under various constraints. Most freeness problems are undecidable starting from dimension three, even for upper-triangular integer matrices. A recent paper investigated freeness properties of bounded languages of matrices, which are matrices from a set M1⁎M2⁎⋯Mk⁎⊆Fn×n for some semiring F and fixed k∈N>0.We consider a notion of freeness and ambiguity for scalar reachability problems in matrix semigroups and bounded languages of matrices. Scalar reachability concerns the set {ρTMτ|M∈S}, where ρ,τ∈Fn are vectors and S⊆Fn×n is a finitely generated matrix semigroup. Ambiguity and freeness problems are defined in terms of the uniqueness of factorizations for each scalar. We show various undecidability results and connections to weighted and probabilistic finite automata.

Reachability and controllability analysis of probabilistic finite automata via a novel matrix method

AbstractProbabilistic finite automata (PFAs) can exhibit a stochastic behavior, and its reachability and controllability is viewed as the first necessary step of supervisory control and stabilization. In this paper, the problems of reachability and controllability of PFAs are investigated under the framework of semi‐tensor product (STP) of matrices. First, a matrix‐based modeling approach to PFAs is proposed, and the dynamics of PFAs can be described as a discrete‐time bilinear expression. Meanwhile, the notions of reachability with a probability of one is formally defined, and F‐reachability with a probability of one is introduced. With the algebraic expression, necessary and sufficient conditions of such reachability are provided systematically. Second, F‐set controllability with a probability of one of PFAs is developed by introducing the F‐reachability with a probability of one, and the associated algebraic condition to verify such controllability are given. Finally, a simple example is illustrated to validate the proposed results.

Advanced Driving Behavior Analytics for an Improved Safety Assessment and Driver Fingerprinting

The recent computerizations of cars, together with the development of sensor technologies and car communication devices have transformed the cars into wealthy sources of information. The analysis of data generated continuously by cars can contribute greatly in improving driving safety and drivers comfort. Even though different analytical solutions have emerged recently, there still exist some important issues in driving safety that we assume were poorly addressed, as well as diverse mathematical methodologies whose application in driving behavior analysis is to be investigated. In this paper, we developed a methodology to process and analyze car-generated data, with focus on two analysis goals: 1) automatic verification of drivers’ behavior conformity to traffic rules; and 2) visualization and comparison of drivers’ behaviors. The proposed methodology is divided into three steps. At first, the abstraction using numerical domains is used to reduce the size of the generated data. Then, the probabilistic graphical models (Probabilistic Automata, and Labeled Directed Graphs) combined with a machine-learning algorithm are used for building a formal model of the driver behavior. Finally, two indepth analyses are carried out by applying automatic model checking and graph matching techniques. Early experimental results point out that the design of numerical domains considered influences hugely the analysis results.

Deciding probabilistic simulation between probabilistic pushdown automata and finite-state systems

Checking whether a pushdown automaton is simulated – in the sense of a simulation pre-order – by a finite-state automaton is EXPTIME-complete. This paper shows that the same computational complexity is obtained in a probabilistic setting. That is, the problem of deciding whether a probabilistic pushdown automaton (pPDA) is simulated by a finite Markov decision process (MDP) is EXPTIME-complete. The considered pPDA contain both probabilistic and non-deterministic branching. The EXPTIME-membership is shown by combining a partition-refinement algorithm with a tableaux system that is inspired by Stirling's technique for bisimilarity checking of ordinary pushdown automata. The hardness is obtained by exploiting the EXPTIME-hardness for the non-probabilistic case. Moreover, our decision problem is in PTIME when both the number of states of the pPDA and the number of states in the MDP are fixed.

Simultaneous Detection of Multiple Appliances From Smart-Meter Measurements via Multi-Label Consistent Deep Dictionary Learning and Deep Transform Learning

Currently there are several well-known approaches to non-intrusive appliance load monitoring—rule based, stochastic finite state machines, neural networks, and sparse coding. Recently several studies have proposed a new approach based on multi-label classification. Different appliances are treated as separate classes, and the task is to identify the classes given the aggregate smart-meter reading. Prior studies in this area have used off-the-shelf algorithms like multi label ${K}$ nearest neighbor and random ${K}$ -label sets to address this problem. In this paper, we propose a deep learning-based technique. There are hardly any studies in deep learning based multi-label classification; two new deep learning techniques to solve the said problem are fundamental contributions of this paper. These are deep dictionary learning and deep transform learning. Thorough experimental results on benchmark datasets show marked improvement over existing studies.

Advanced aspects of Galactic habitability

Context. Astrobiological evolution of the Milky Way (or the shape of its “astrobiological landscape”) has emerged as a key research topic in recent years. In order to build precise, quantitative models of the Galactic habitability, we need to account for two opposing tendencies of life and intelligence in the most general context: the tendency to spread to all available ecological niches (conventionally dubbed “colonization”) and the tendency to succumb to various types of existential catastrophes (“catastrophism”). These evolutionary tendencies have become objects of study in fields such as ecology, macroevolution, risk analysis, and futures studies, though a serious astrobiological treatment has so far been lacking.Aims. Our aim is to numerically investigate the dynamics of opposed processes of expansion (panspermia, colonization) and extinction (catastrophic mechanisms) of life in the Galaxy.Methods. We employed a new type of numerical simulation based on 1D probabilistic cellular automaton with very high temporal resolution, in order to study astrobiological dynamics.Results. While the largest part of the examined parameter space shows very low habitability values, as expected, the remaining part has some observationally appealing features that imply, among other things, a reduction in the amount of fine-tuning necessary for resolving the Fermi paradox.Conclusions. Advanced aspects of Galactic habitability are amenable to precision studies using massive parallel computer simulations. There are regions of the parameter space that correspond to a quasi-stationary state satisfying observable constraints and possessing viable SETI targets.

Semitensor Product Approach to Controllability, Reachability, and Stabilizability of Probabilistic Finite Automata

This paper proposes a matrix-based approach to investigate the controllability, reachability, and stabilizability of probabilistic finite automata (PFA). Firstly, the state transition probabilistic structure matrix is constructed for PFA, based on which a kind of controllability matrix is defined for PFA. Secondly, some necessary and sufficient conditions are presented for the controllability, reachability, and stabilizability of PFA with positive probability by using the controllability matrix. Finally, an illustrate example is given to validate the obtained new results.

An investigative design of optimum stochastic language model for bangla autocomplete

<p class="Abstract">Word completion and word prediction are two important phenomena in typing that have extreme effect on aiding disable people and students while using keyboard or other similar devices. Such autocomplete technique also helps students significantly during learning process through constructing proper keywords during web searching. A lot of works are conducted for English language, but for Bangla, it is still very inadequate as well as the metrics used for performance computation is not rigorous yet. Bangla is one of the mostly spoken languages (3.05% of world population) and ranked as seventh among all the languages in the world. In this paper, word prediction on Bangla sentence by using stochastic, i.e. <em>N</em>-gram based language models are proposed for autocomplete a sentence by predicting a set of words rather than a single word, which was done in previous work. A novel approach is proposed in order to find the optimum language model based on performance metric. In addition, for finding out better performance, a large Bangla corpus of different word types is used.</p>

MODELLING THE DYNAMICS OF THE SUBJECT OF MASS COMMUNICATION MENTALITY

The paper outlines the modelling concept of the dynamics of susceptibility of the subjects of mass communication to the effects of inductors. The level of susceptibility is one of the key characteristics of the subject's mentality, as a system of feelings (likes and dislikes), stereotypes, values, ideas about the world, which are formed in the mind during key periods of his life (childhood, becoming, social and political disasters, etc.). The changes in the structure of this system, its key characteristics – levels of perception, as well as the impact (induction) of certain views on social phenomena are determined as the dynamics of mentality. The probability of transition of the recipient from one socio-psychological state to another depends on the levels of perception and influence in a pair of recipient-inductor. Such dependence is adopted as multiplicative. Transitions from state to state under the influence of various factors may be accompanied by changes in the levels of perception and impact, which are determined by the dynamics of mentality. Mathematical models of this dynamics are offered in the form of iterative schemes, finite probabilistic automata. The states themselves can be viewed as structures (vectors, in particular), their components (impact and perception levels, types of behavior, in particular) - as linguistic variables that take on the values of vague variables, which, in turn, are determined by the characteristic functions of vague sets. It was determined that iterative schemes should be applied with variability (possible changes) of the state structure, dynamism of the set of states (some states are not known in advance, possible emergence of new states). For impact and susceptibility levels (the number of which, in case of using a vague option, is limited and known in advance, for example, zero, low, medium, high, maximum), it is recommended to use finite probabilistic automata. Fixing the transition from state to state can be carried out by sociological tools (by interviewing, questioning, etc.).

Homomorphic images and shuffle product on probabilistic automata

A probabilistic automaton (pa) is a fuzzy automaton, in which, sum of all fuzzy memberships of the initial states is one and from each state, on an input symbol, the sum of the fuzzy memberships of the transitions is one. In pa, it is shown that, if h : Γ* → Σ* is a morphism and h–1 (λ) = λ, then the image of a recognisable subset of Γ* is a recognisable subset of Σ* and if h is fine, then the inverse image of recognisable subset of Σ* is recognisable. It is also proved that the shuffle product of any two recognisable sets is recognisable.

Homomorphic images and shuffle product on probabilistic automata

Homomorphic images and shuffle product on probabilistic automata

Three-dimensional cellular automaton model for the destruction of brittle heterogeneous materials

The article investigates the evolution modes of cluster damage structure in brittle heterogeneous materials by using a three-dimensional probabilistic cellular automaton. By comparing the data of computer and physical experiments, there was established the essential role of the model parameter, which describes the intensity of the material destruction process under the influence of local overstress near the existing damage clusters - the probability of perimeter germination. The comparison of kinetic curves of damage accumulation and correlation functions showed that, depending on the probability value for damage cluster perimeter germination, two qualitatively different modes of evolution of damage accumulation process are observed. In this case, the best correspondence of correlation functions in model and physical experiment on pulsed electromagnetic emission is observed for perimeter germination probability values smaller than 0.2.

Competition for resources may reinforce the evolution of altruism in spatially structured populations.

Spatial structure is known to affect the evolution of social behaviour, but little is known on how this evolution depends on simultaneous competition for resources. In simple models, competition for resources tends to counteract altruism, but ecologically more realistic models suggest that competition for resources might actually reinforce altruism. Here we set up a probabilistic cellular automaton (PCA) model and analyse it using the Correlation Dynamics (CD) approach, to study how competition for resources affects the evolution of altruism. If the resource diffuses across space, spatiallyseparateclustersofrelativesmaystillcompeteforresources, thuscreatingalargercompetitive kernelthantheimmediateneighbourhood. Thisincreasestheseparationofclustersofrelativesandthus reinforces the selection of altruistic behaviour.

Using probabilistic fuzzy models for the prediction of functional failures of microwave LSI with radiation exposure

The article presents an analysis of microwave LSI behavior under radiation exposure at the functional-logical level of description. The analysis is based on fuzzy digital automaton and topological probabilistic models of workability assessment. It is shown that in certain cases both deterministic and non-deterministic failures are typical. Each operation threshold in logic elements under radiation influence has a zone of uncertainty and can be expressed quantitatively by a fuzzy number. This case, the real nature of microwave LSI radiation behavior is determined by the specific ratio of radiation-sensitive parameters of its elements and by taking into account the influence of their statistical scatter. Methods are proposed for simulating failures of microwave LSI under radiation exposure that are based on the model of a fuzzy digital Brauer automaton and a probabilistic reliability automaton.

Analysis of quantitative characteristics of microstructures synthesized by method of probabilistic cellular automata

Analysis of quantitative characteristics of microstructures synthesized by method of probabilistic cellular automata

SIRS-модель распространения инфекций с динамическим регулированием численности популяции: Исследование методом вероятностных клеточных автоматов

SIRS-модель распространения инфекций с динамическим регулированием численности популяции: Исследование методом вероятностных клеточных автоматов

Development of anomalous computer behavior detection method based on probabilistic automaton

The paper proposes a method for identifying the anomalous behavior of a computer system based on probabilistic automaton. The main components of the method are the model of generation of the structure of the automaton and its modification procedure. The defining feature of the method is adaptation of automaton structure generation procedure for detecting scenarios of the same type, by restructuring the structure of the automaton upon a match and by recalculation of the state transition probabilities. Input data of the automaton consist of discrete events (system calls, process IDs or sections of code instructions), typical for a certain class of anomalous behavior, and grouped by type. The automaton structure is first created in accordance with one of the instances of a class, and then restructured during the analysis of other instances. Possibility of state transition depends on the input state and transition probability value. Generated automaton structure is used to detect anomalous computer system behavior. Automaton structure can be updated, if an anomaly occurs with different scenarios. Proposed method allows to speed up detecting anomalous computer behavior, as well as to detect computer system anomalies, scenario profiles of which only partially match with instances used for generation the structure of the automaton. Obtained research results allow us to conclude about the possibility of using this method in heuristic analyzers of anomaly detection systems.

AUTOMATON: A Program That Combines a Probabilistic Cellular Automata and a Genetic Algorithm for Global Minimum Search of Clusters and Molecules.

A novel program for the search of global minimum structures of atomic clusters and molecules in the gas phase, AUTOMATON, is introduced in this work. This program involves the following: first, the generation of an initial population, using a simplified probabilistic cellular automaton method, which allows easy control of the adequate distribution of atoms in space; second, the fittest individuals are selected to evolve, through genetic operations (mating and mutations), until the best candidate for a global minimum surfaces. In addition, we propose a simple way to build the descendant structures by establishing a ranking of genes to be inherited. Thus, by means of a chemical formula checker procedure, genes are transferred to the offspring, ensuring that they always have the appropriate type and number of atoms. It is worth noting that a fraction of the fittest group is subject to mutation operations. This program also includes algorithms to identify duplicate structures: one based on geometric similarity and another on the similar distribution of atomic charges. The effectiveness of the program was evaluated in a group of 45 molecules, considering organic and organometallic compounds (benzene, cyclopentadienyl anion, and ferrocene), Zintl ion clusters [Sn9- m- nGe mBi n](4- n)- ( n = 1-4 and m = 0-(9- n)), star-shaped clusters (Li7E5+, E = BH, C, Si, Ge) and a variety of boron-based clusters. The global minimum and the lowest-energy isomers reported in the literature were found for all the cases considered in this article. These results successfully prove AUTOMATON's effectiveness on the identification of energetically preferred structures of a wide variety of chemical species.

Stochastic pretopology as a tool for complex networks analysis

ABSTRACTWe are proposing in this work a novel approach for complex network analysis by introducing Stochastic Pretopology, a result of the combination of Pretopology theory and Random Sets. We firstly show how pretopology generalizes the graph theory to deal with complex interactions in complex networks. By connecting with random set theory, we then give the definition of stochastic pretopology and also propose the ways to build this kind of pretopology in many situations. That is to say how proximity with randomness can be delivered to model complex neighbourhoods formation in complex networks. In addition, we also show how stochastic pretopology can be applied for modelling dynamic processes on complex networks by representing classical information diffusion models under stochastic pretopology language and then proposing Pretopology Cascade Model as a general model for information diffusion process that can take place in more complex networks such as multi-relational networks or stochastic graphs.