Martingale problem approach to Markov processes

... processes, then the results on stationary distributions and evolution equations are true. These extensions were crucial for application to Filtering theory. Kallianpur, Karandikar and Bhatt used these results to prove that Fujisaki-Kallianpur-Kunita equation and Zakai equation (these are infinite di ...

... processes, then the results on stationary distributions and evolution equations are true. These extensions were crucial for application to Filtering theory. Kallianpur, Karandikar and Bhatt used these results to prove that Fujisaki-Kallianpur-Kunita equation and Zakai equation (these are infinite di ...

An efficient algorithm for the blocked pattern matching problem

... In this subsection, we present an efficient algorithm for the BPM problem, in which the text T is represented by a suffix tree. Although the proposed algorithm works for suffix trees in which each edge is labeled with a text string with one or more letters, here we assume that each edge is labeled w ...

... In this subsection, we present an efficient algorithm for the BPM problem, in which the text T is represented by a suffix tree. Although the proposed algorithm works for suffix trees in which each edge is labeled with a text string with one or more letters, here we assume that each edge is labeled w ...

Query rewriting and answering under constraints in data integration

... 1. B is consistent with G, i.e., it satisfies the IDs in ΣI and the KDs in ΣK . More formally: (i) B satisfies an inclusion dependency r1 [A] ⊆ r2 [B] if for each tuple t1 in r1B there exists a tuple t2 in r2B such that t1 [A] = t2 [B], where t[A] is the projection of the tuple t over A. If B satisf ...

... 1. B is consistent with G, i.e., it satisfies the IDs in ΣI and the KDs in ΣK . More formally: (i) B satisfies an inclusion dependency r1 [A] ⊆ r2 [B] if for each tuple t1 in r1B there exists a tuple t2 in r2B such that t1 [A] = t2 [B], where t[A] is the projection of the tuple t over A. If B satisf ...

MOD p LOGARITHMS log2 3 AND log3 2 DIFFER FOR

... We may consider a generalization of problem 2 into the setting of group schemes. Let A/Q be an abelian group scheme over Q (we understand under this notion a group scheme [B] whose group structure is abelian without further restrictions, cf. [Mi] for narrower definition), with some reasonably good m ...

... We may consider a generalization of problem 2 into the setting of group schemes. Let A/Q be an abelian group scheme over Q (we understand under this notion a group scheme [B] whose group structure is abelian without further restrictions, cf. [Mi] for narrower definition), with some reasonably good m ...

# Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other. A computational problem is understood to be a task that is in principle amenable to being solved by a computer, which is equivalent to stating that the problem may be solved by mechanical application of mathematical steps, such as an algorithm.A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying the amount of resources needed to solve them, such as time and storage. Other complexity measures are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computational complexity theory is to determine the practical limits on what computers can and cannot do.Closely related fields in theoretical computer science are analysis of algorithms and computability theory. A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem, whereas the latter asks a more general question about all possible algorithms that could be used to solve the same problem. More precisely, it tries to classify problems that can or cannot be solved with appropriately restricted resources. In turn, imposing restrictions on the available resources is what distinguishes computational complexity from computability theory: the latter theory asks what kind of problems can, in principle, be solved algorithmically.