Minimization of Reactive Probabilistic Automata

The problem of finite automata minimization is important for software and hardware designing. Different types of automata are used for modeling systems or machines with finite number of states. The limitation of number of states gives savings in resources and time. In this article we show specific type of probabilistic automata: the reactive probabilistic finite automata with accepting states (in brief the reactive probabilistic automata), and definitions of languages accepted by it. We present definition of bisimulation relation for automata's states and define relation of indistinguishableness of automata states, on base of which we could effectuate automata minimization. Next we present detailed algorithm reactive probabilistic automata’s minimization with determination of its complexity and analyse example solved with help of this algorithm.

Detection of Logical-and-Probabilistic Correlation in Time Series

An application of the heterogeneous variables system prediction method to solving the time series analysis problem with respect to the sample size is considered in this work. It is created a logical-and-probabilistic correlation from the logical decision function class. Two ways is considered. When the information about event is kept safe in the process, and when it is kept safe in depending process.

Self-organizing Map and Cellular Automata Combined Technique for Advanced Mesh Generation in Urban and Architectural Design

This paper presents a technique for building complex and adaptive meshes for urban and architectural design. The combination of a self-organizing map and cellular automata algorithms stands as a method for generating meshes otherwise static. This intends to be an auxiliary tool for the architect or the urban planner, improving control over large amounts of spatial information. The traditional grid employed as design aid is improved to become more general and flexible.

Applications of Nonclassical Logic Methods for Purposes of Knowledge Discovery and Data Mining

* The work is partially supported by Grant no. NIP917 of the Ministry of Science and Education – Republic of Bulgaria.

Построение Логико-Вероятностных Моделей Временных Рядов с Использованием Цепей Маркова

The method of logic and probabilistic models constructing for multivariate heterogeneous time series is offered. There are some important properties of these models, e.g. universality. In this paper also discussed the logic and probabilistic models distinctive features in comparison with hidden Markov processes. The early proposed time series forecasting algorithm is tested on applied task.

Timed Transition Automata as Numerical Planning Domain

A general technique for transforming a timed finite state automaton into an equivalent automated planning domain based on a numerical parameter model is introduced. Timed transition automata have many applications in control systems and agents models; they are used to describe sequential processes, where actions are labelling by automaton transitions subject to temporal constraints. The language of timed words accepted by a timed automaton, the possible sequences of system or agent behaviour, can be described in term of an appropriate planning domain encapsulating the timed actions patterns and constraints. The time words recognition problem is then posed as a planning problem where the goal is to reach a final state by a sequence of actions, which corresponds to the timed symbols labeling the automaton transitions. The transformation is proved to be correct and complete and it is space/time linear on the automaton size. Experimental results shows that the performance of the planning domain obtained by transformation is scalable for real world applications. A major advantage of the planning based approach, beside of the solving the parsing problem, is to represent in a single automated reasoning framework problems of plan recognitions, plan synthesis and plan optimisation.

Probabilistic Models in Cryptography, Coding Theory and Tests for PRNG

2000 Mathematics Subject Classification: 94A29, 94B70

Weak and Semi Compatible Maps in Probabilistic Metric Space Using Implicit Relation

2000 Mathematics Subject Classification: 54H25, 47H10.

Conceptual Foundations of Construction of the Models and Procedures for Prediction of the Avalanche-dangerous Situations Initiation

The conceptual foundations of the models and procedures for prediction of the avalanche-dangerous situations initiation are considered. The interpretation model for analysis of the avalanche-dangerous situations initiation based on the definition of probabilities of correspondence of studied parameters to the probabilistic distributions of avalanche-dangerous or avalanche non-dangerous situations is offered. The possibility to apply such a model to the real data is considered. The main approaches to the use of multiple representations for the avalanche dangerous situations initiation analysis are generalized.

Ontology View on Automata Theory

The summary of automata theory ontology is presented in the paper. It is based on the following dependences: a type of an automaton – the language accepted by the automaton – applications. The given ontology does not claim to be exhaustive as automata theory is very extensive and it is a complicated problem to survey all its aspects within one article. Only the main properties of automata and their applications are considered.

Conceptual Information Compression and Efficient Pattern Search

This paper introduces an encoding of knowledge representation statements as regular languages and proposes a two-phase approach to processing of explicitly declared conceptual information. The idea is presented for the simple conceptual graphs where conceptual pattern search is implemented by the so called projection operation. Projection calculations are organised into off-line preprocessing and run-time computations. This enables fast run-time treatment of NP-complete problems, given that the intermediate results of the off-line phase are kept in suitable data structures. The experiments with randomly-generated, middle-size knowledge bases support the claim that the suggested approach radically improves the run-time conceptual pattern search.

On OBDD Transformations Representing Finite State Automata

We present OBDD transformation problem representing finite labeled transition systems corresponding to some congruence relation. Transformations are oriented toward obtaining the OBDD of a minimized transition system for this congruence relation.

On Handling Replay Attacks in Intrusion Detection Systems

We propose a method for detecting and analyzing the so-called replay attacks in intrusion detection systems, when an intruder contributes a small amount of hostile actions to a recorded session of a legitimate user or process, and replays this session back to the system. The proposed approach can be applied if an automata-based model is used to describe behavior of active entities in a computer system.

Approximate Model Checking of Real-Time Systems for Linear Duration Invariants

Real-time systems are usually modelled with timed automata and real-time requirements relating to the state durations of the system are often specifiable using Linear Duration Invariants, which is a decidable subclass of Duration Calculus formulas. Various algorithms have been developed to check timed automata or real-time automata for linear duration invariants, but each needs complicated preprocessing and exponential calculation. To the best of our knowledge, these algorithms have not been implemented. In this paper, we present an approximate model checking technique based on a genetic algorithm to check real-time automata for linear durration invariants in reasonable times. Genetic algorithm is a good optimization method when a problem needs massive computation and it works particularly well in our case because the fitness function which is derived from the linear duration invariant is linear. ACM Computing Classification System (1998): D.2.4, C.3.

Some Probabilistic Results in a Bisexual Branching Process with Immigration

2000 Mathematics Subject Classification: 60J80.