New PDF release: Automata for Branching and Layered Temporal Structures: An

By Gabriele Puppis

ISBN-10: 3642118801

ISBN-13: 9783642118807

Since 2002, FoLLI awards an annual prize for a great dissertation within the fields of good judgment, Language, and knowledge. This ebook is predicated at the Ph.D. thesis of Gabriele Puppis, who was once the winner of the E.W. Beth dissertation award for 2007.

Puppis' thesis specializes in good judgment and Computation and, extra particularly, on automata-based decidability thoughts for time granularity and on a brand new technique for finding out Monadic moment Order theories of timber. the implications awarded characterize an important step in the direction of a greater realizing of the alterations in granularity degrees that people make so simply in cognition of time, area, and different phenomena, while their logical and computational constitution poses tough conceptual and computational challenges.

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2 that search for occurrences of distinguished symbols in the word recognized by a given NCSSA A. As an example, the following procedure, 34 2 Word Automata and Time Granularities receives as input an NCSSA A, a set B of symbols, a natural number n, and two positions i, j ∈ N ∪ {ω} and, after O( A ) time, it returns as output the position of the n-th occurrence of a symbol in B in the substring w[i, j[, where w is the word recognized by A (if n = 0, then the procedure returns the position i). 3.

Let x be the finite word recognized by B , q the minimum period of x, and r = k |x|. Furthermore, let B be a complexity optimal NCSSA that recognizes the prefix w[1, q] of w and let C be a complexity optimal NCSSA that recognizes the suffix w[r+1, |w|] of w. Clearly, we have q |x|. Since w[1, q] is a prefix of x and B is a complexity optimal NCSSA that recognizes w[1, q], by Lemma 5, we obtain B B . Moreover, since C is a complexity optimal NCSSA equivalent to C , we obtain C C . Therefore, we have AppendRepetition(B, r/q, C) =1 + max B , C 1 + max B , C = AppendRepetition(B , k, C ) = A .

2 and the principle of γ-induction, one can prove that the value A s is less than or + + equal to the number of pairs (q, r) ∈ ΓA such that either r = s or (r, s) ∈ ΓA . It is thus clear that the complexity A of A is at most quadratic in the number of states of A and hence we can write A = O(|A|2 ). 2 is Θ( A ) (and hence it is at most quadratic in the size |A|). It turns out that the running time of several algorithms operating on NCSSA run in linear time with respect to the complexities of the involved automata.

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Automata for Branching and Layered Temporal Structures: An Investigation into Regularities of Infinite Transition Systems by Gabriele Puppis

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