256,146 research outputs found

    Formal Languages in Dynamical Systems

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    We treat here the interrelation between formal languages and those dynamical systems that can be described by cellular automata (CA). There is a well-known injective map which identifies any CA-invariant subshift with a central formal language. However, in the special case of a symbolic dynamics, i.e. where the CA is just the shift map, one gets a stronger result: the identification map can be extended to a functor between the categories of symbolic dynamics and formal languages. This functor additionally maps topological conjugacies between subshifts to empty-string-limited generalized sequential machines between languages. If the periodic points form a dense set, a case which arises in a commonly used notion of chaotic dynamics, then an even more natural map to assign a formal language to a subshift is offered. This map extends to a functor, too. The Chomsky hierarchy measuring the complexity of formal languages can be transferred via either of these functors from formal languages to symbolic dynamics and proves to be a conjugacy invariant there. In this way it acquires a dynamical meaning. After reviewing some results of the complexity of CA-invariant subshifts, special attention is given to a new kind of invariant subshift: the trapped set, which originates from the theory of chaotic scattering and for which one can study complexity transitions.Comment: 23 pages, LaTe

    Non-Deterministic Communication Complexity of Regular Languages

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    In this thesis, we study the place of regular languages within the communication complexity setting. In particular, we are interested in the non-deterministic communication complexity of regular languages. We show that a regular language has either O(1) or Omega(log n) non-deterministic complexity. We obtain several linear lower bound results which cover a wide range of regular languages having linear non-deterministic complexity. These lower bound results also imply a result in semigroup theory: we obtain sufficient conditions for not being in the positive variety Pol(Com). To obtain our results, we use algebraic techniques. In the study of regular languages, the algebraic point of view pioneered by Eilenberg (\cite{Eil74}) has led to many interesting results. Viewing a semigroup as a computational device that recognizes languages has proven to be prolific from both semigroup theory and formal languages perspectives. In this thesis, we provide further instances of such mutualism.Comment: Master's thesis, 93 page

    State Complexity of Combined Operations on Finite Languages

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    State complexity is a descriptive complexity measure for regular languages. It is a fundamental topic in automata and formal language theory. The state complexity of a regular language is the number of states in the minimal complete deterministic finite automaton accepting the language. During the last few decades, many publications have focused and studied the state complexity of many individual as well as combined operations on regular languages. Also, the state complexity of some basic operations on finite languages has been studied. But until now there has been no study on the state complexity of combined operations on finite languages. In this thesis, we will first study the state complexity of the combined operation, star of union, on finite languages and give an exact bound. Then we will investigate the state complexity of star of catenation and show its approximation with a good ratio bound and finally, we will prove an upper bound for star of intersection

    Digraph Complexity Measures and Applications in Formal Language Theory

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    We investigate structural complexity measures on digraphs, in particular the cycle rank. This concept is intimately related to a classical topic in formal language theory, namely the star height of regular languages. We explore this connection, and obtain several new algorithmic insights regarding both cycle rank and star height. Among other results, we show that computing the cycle rank is NP-complete, even for sparse digraphs of maximum outdegree 2. Notwithstanding, we provide both a polynomial-time approximation algorithm and an exponential-time exact algorithm for this problem. The former algorithm yields an O((log n)^(3/2))- approximation in polynomial time, whereas the latter yields the optimum solution, and runs in time and space O*(1.9129^n) on digraphs of maximum outdegree at most two. Regarding the star height problem, we identify a subclass of the regular languages for which we can precisely determine the computational complexity of the star height problem. Namely, the star height problem for bideterministic languages is NP-complete, and this holds already for binary alphabets. Then we translate the algorithmic results concerning cycle rank to the bideterministic star height problem, thus giving a polynomial-time approximation as well as a reasonably fast exact exponential algorithm for bideterministic star height.Comment: 19 pages, 1 figur

    Adaptive Intelligent Tutoring System for learning Computer Theory

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    In this paper, we present an intelligent tutoring system developed to help students in learning Computer Theory. The Intelligent tutoring system was built using ITSB authoring tool. The system helps students to learn finite automata, pushdown automata, Turing machines and examines the relationship between these automata and formal languages, deterministic and nondeterministic machines, regular expressions, context free grammars, undecidability, and complexity. During the process the intelligent tutoring system gives assistance and feedback of many types in an intelligent manner according to the behavior of the student. An evaluation of the intelligent tutoring system has revealed reasonably acceptable results in terms of its usability and learning abilities are concerned

    Advanced Topics on State Complexity of Combined Operations

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    State complexity is a fundamental topic in formal languages and automata theory. The study of state complexity is also strongly motivated by applications of finite automata in software engineering, programming languages, natural language and speech processing and other practical areas. Since many of these applications use automata of large sizes, it is important to know the number of states of the automata. In this thesis, we firstly discuss the state complexities of individual operations on regular languages, including union, intersection, star, catenation, reversal and so on. The state complexity of an operation on unary languages is usually different from that of the same operation on languages over a larger alphabet. Both kinds of state complexities are reviewed in the thesis. Secondly, we study the exact state complexities of twelve combined operations on regular languages. The state complexities of most of these combined operations are not equal to the compositions of the state complexities of the individual operations which make up these combined operations. We also explore the reason for this difference. Finally, we introduce the concept of estimation and approximation of state complexity. We show close estimates and approximations of the state complexities of six combined operations on regular languages which are good enough to use in practice
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