For a Markovian source, we analyze the Lempel-Ziv parsing scheme that partitions sequences into phrases such that a new phrase is the shortest phrase not seen in the past. We consider three models: In the Markov Independent model, several sequences are generated independently by Markovian sources, and the ith phrase is the shortest preex of the ith sequence that was not seen before as a phrase ...

We look at extensions (i.e., stronger logics in the same language) of the Belnap-Dunn four-valued logic. We prove the existence of a countable chain of logics that extend the Belnap-Dunn and do not coincide with any of the known extensions (Kleene’s logics, Priest’s logic of paradox). We characterize the reduced algebraic models of these new logics and prove a completeness result for the first ...

We the compare the number of phrases created by Ziv/Lempel '78 parsing of a binary sequence and of its reversal. We show that the two parsings can vary by a factor that grows at least as fast as the logarithm of the sequence length. We then show that under a suitable condition, the factor can even become polynomial, and argue that the condition may not be necessary.

Jing Tang Microsoft Corporation One Microsoft Way, 1/2061 Redmond, WA 98052 U.S.A. [email protected] For a Markovian source, we analyze the Lempel-Ziv parsing scheme that partitions sequences into phrases such that a new phrase is the shortest phrase not seen in the past. We consider three models: In the Markov Independent model, several sequences are generated independently by Markovian sou...

This paper addresses the problem of probabilistic reasoning as it applies to Truth Maintenance Systems. A Belief Maintenance System hal! been constructed which manages a current set of probabilistic beliefs in much the same way that a TMS manages a set of true/false beliefs. Such a system may be thought of as a generalization of a. Truth Maintenance System. It enables one to reason using normal...

Bilattices and d-frames are two different kinds of structures with a four-valued interpretation. Whereas d-frames were introduced with their topological semantics in mind, the theory of bilattices has a closer connection with logic. We consider a common generalisation of both structures and show that this not only still has a clear bitopological semantics, but that it also preserves most of the...

This paper looks at logic programming with three kinds of negation: default, weak and strict negations. A 3-valued logic model theory is discussed for logic programs with three kinds of negation. The procedure is constructed for negations so that a soundness of the procedure is guaranteed in terms of 3-valued logic model theory.

A word w is said to be closed if it has a proper factor x which occurs exactly twice in w, as prefix and suffix of w. Based on the concept Ziv–Lempel factorization, we define z-factorization finite infinite words. Then find m-bonacci words for all m≥2. We also classify prefixes