From a sequence {ai}i0 over GF(p) with period pn-1 we can obtain another periodic sequence {i}i0 with period pn-2 by deleting one symbol at the end of each period. We will give the bounds (upper bound and lower bound) of linear complexity of {i}i0 as a typical example of instability of linear complexity. Derivation of the bounds are performed by using the relation of characteristic polynomials between {ai}i0 and {ai(j)}i0={ai+j}i0, jGF(p){0}. For a binary m-sequence {ai}i0 with period 2n-1, n-1 a prime, we will give the explicit formula for the characteristic polynomial of {i}i0.

Viterbi decoding is known as a decoding scheme that can realize maximum likelihood decoding. However, it is impossible to continue it without re-synchronization even if only an insertion/deletion error occurs in a channel. In this paper, we show that Levenshtein distance is suitable for the metric of Viterbi decoding in a channel where not only symbol errors but also insertion/deletion errors occur under some conditions and we propose a kind of Viterbi decoding considering insertion/deletion errors.

The subject of the paper is to analyze time complexity of the minimum modification problem in the Horn clause propositional logic. Given a set H of Horn clauses and a query Q in propositional logic, we say that Q is provable over H if and only if Q can be shown to be true by repeating Modus Ponens among clauses of H. Suppose that Q is not provable over H, and we are going to modify H and Q into H and Q , respectively, such that Q is provable over H . The problem of making such modification by minimum variable deletion (MVD), by minimum clause addition (MCA) or by their combination (MVDCA) is considered. Each problem is shown to be NP-complete, and some approximation algorithms with their experimental evaluation are given.