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We use automata-theoretic approach to analyze properties of Fibonacci words. The directed acyclic subword graph (dawg) is a useful deterministic automaton accepting all suffixes of the word. We show that dawg’s of Fibonacci words have particularly simple structure. The simple structure of paths in these graphs gives simplified alternative proofs and new interpretation of several known properties of Fibonacci words. The structure of lengths of paths in the compacted subword graph corresponds to a number-theoretic characterization of occurrences of subwords in terms of Zeckendorff Fibonacci number system. Using the structural properties of dawg’s it can be easily shown that for a string we can check if is a subword of a Fibonacci word in time (||) and (1) space. Compact dawg’s of Fibonacci words show a very regular structure of their suffix trees and show how the suffix tree for the Fibonacci word grows (extending the leaves in a very simple way) into the suffix tree for the next Fibonacci word.

The two determinization procedures of Safra and Muller-Schupp for Büchi automata are compared, based on an implementation in a program called OmegaDet.

We solve the ‘order preserving’ version of the generalized Černý problem (also known as the rank problem). Namely, for all and such that 2 ≤ ≤ , we determine the least number ℓ(,) such that for each monotonic automaton with states and interval rank there exists a word of length ℓ(,) that compresses the state set of the automaton to an interval of length .

We propose a scheme for automatically generating compressors for XML documents from Document Type Definition(DTD) specifications. Our algorithm is a lossless adaptive algorithm where the model used for compression and decompression is generated automatically from the DTD, and is used in conjunction with an arithmetic compressor to produce a compressed version of the document. The structure of the model mirrors the syntactic specification of the document. Our compression scheme is on-line, that is, it can compress the document as it is being read. We have implemented the compressor generator, and provide the results of experiments on some large XML databases whose DTD’s are specified. We note that the average compression is better than that of XMLPPM, the only other on-line tool we are aware of. The tool is able to compress massive documents where XMLPPM failed to work as it ran out of memory. We believe the main appeal of this technique is the fact that the underlying model is so simple and yet so effective.

Checking tree automata containment is a fundamental operation in static verification of XML processing programs. However, tree automata containment problem is known to be EXPTIME-complete and a standard algorithm with determinization of automata easily blows up even in practical cases. Hosoya, Vouillon, and Pierce have proposed a top-down algorithm that efficiently works for a large class of typical instances. However, there still remains a considerable inefficiency because of repeated calculation incurred by backtracking. In this paper, we propose a top-down algorithm which improves this inefficiency. In the algorithm, we introduce “dependencies” among performed computations and, by exploiting these, we can recover certain kinds of information lost by backtracking. One difficulty in constructing such algorithm is, however, that, since some dependency information can be useless, we may be misled to needless computation by using such information. To alleviate this problem, we carefully check the usefulness of each dependency whenever we use it. Since these checks introduce a subtlety to our algorithm, we rigorously formalize it with a correctness proof. Our preliminary experiments show that our algorithm works more efficiently compared to the previous algorithm.

We present a method for size reduction of two-way multitape automata. Our algorithm applies local transformations that change the order in which transitions concerning different tapes occur in the automaton graph, and merge suitable states into a single state. Our work is motivated by implementation of a language for string manipulation in database systems where string predicates are compiled into two-way multitape automata. Additionally, we present a (one-tape) NFA reduction algorithm that is based on a method proposed for DFA minimization by Kameda and Weiner, and apply this algorithm, combined with the multitape automata reduction algorithm, on our multitape automata.

The paper introduces a robust spelling correction technique to deal with ill-formed input strings, including unknown parts of unknown length. In contrast to previous works, we derive profit from a finer dynamic programming construction, which takes advantage of the underlying grammatical structure, leading to an improved computational behavior and error repair quality. The formal description applies a deductive approach in order to simplify this task, separating it from the interpretation strategy, and including cut-off facilities.

This paper presents a general concept of two-dimensional pattern matching using conventional (one-dimensional) finite automata. Then two particular models and methods, implementations of the general principle, are presented. The first of these two models presents an automata based version of the Bird and Baker approach with lower space complexity than the original algorithm. The second introduces a new model for two-dimensional approximate pattern matching using the two-dimensional Hamming distance.

Pseudo-minimal automata ([1],[2]) are minimal acyclic automata that have a proper element (a transition or a state) for each word belonging to the language of the automaton. That proper element is not shared with any other word, and it can be used for implementing a function on words belonging to the language. For instance, dynamic perfect hashing (e.g. a mapping from unique words to consecutive numbers, such that addition of new elements does not change the order of the previous elements) can be implemented using a pseudo-minimal automaton ([3]).

Inference of RFSAs has been recently presented [1] as an alternative to inference of DFAs if the target language has been obtained by a random generation of NFAs. We propose in this paper the algorithm RPNI2, which is a variation of the previous RPNI, that also outputs DFAs as hypothesis. The experiments done using the same data as in [1] show that RPNI2 has an error rate very similar to the rate obtained in the inference of RFSAs, but the size of the hypothesis is substantially smaller.