We investigate the magic number problem, that is, the question whether there exists a minimal n-state nondeterministic finite automaton (NFA) whose equivalent minimal deterministic finite automaton (DFA) has α states, for all n and α satisfying n ≤ α ≤ 2n. A number α not satisfying this condition is called a magic number (for n). It was shown in [11] that no magic numbers exist for general regu...

Given a pattern P , a text T , and an integer k, we want to find for every position j of T , the index of the k-mismatch of P with the suffix of T starting at position j. We give an algorithm that finds the exact index for each j, and algorithms that approximate it. We use these algorithms to get an efficient solution for an approximate version of the tandem repeats problem with k-mismatches.

String matching is critical in information retrieval since in many cases information is stored and manipulated as strings. Constructing and utilizing a suitable data structure for a text string, we can solve the string matching problem efficiently. Such a structure is called an index structure. Suffix trees are certainly the most widely-known and extensively-studied structure of this kind. In t...

We give a sound and complete labeled natural deduction system for an interesting fragment of CTL∗, namely the until-free version of BCTL∗. The logic BCTL∗ is obtained by referring to a more general semantics than that of CTL∗, where we only require that the set of paths in a model is closed under taking suffixes (i.e. is suffix-closed) and is closed under putting together a finite prefix of one...

In this paper, we propose an algorithm for computing and maintaining recently frequent patterns which is more stable and smaller than the data stream and dynamically updating them with the incoming transactions. Our study mainly has two contributions. First, a regression-based data stream model is proposed to differentiate new and old transactions. The novel model reflects transactions into man...

We study the problem of finding all k-periods of a length-n string S, presented as a data stream. S is said to have k-period p if its prefix of length n− p differs from its suffix of length n− p in at most k locations. We give a one-pass streaming algorithm that computes the k-periods of a string S using poly(k, logn) bits of space, for k-periods of length at most n 2 . We also present a two-pa...