42293969
Approximate Regular Expression Pattern Matching with Concave Gap Penalties
Given a sequence A of length M and a regular expression R of length P, an approximate regular expression pattern matching algorithm computes the score of the best alignment between A and one of the sequences exactly matched by R. There are a variety of schemes for scoring alignments. In a concave gap-penalty scoring scheme, a function δ(a, b) gives the score of each aligned pair of symbols a and b, and a concave function w(k) gives the score of a sequence of unaligned symbols, or gap, of length k. A function w is concave if and only if it has the property that for all k > 1, w(k+ 1)-w(k) <w(k) — w(k−1). In this paper we present an O(MP(log M + log2P)) algorithm for approximate regular expression matching for an arbitrary δ and any concave w.
14175074
Approximate regular expression pattern matching with concave gap penalties
Given a sequenceA of lengthM and a regular expressionR of lengthP, an approximate regular expression pattern-matching algorithm computes the score of the optimal alignment betweenA and one of the sequencesB exactly matched byR. An alignment between sequencesA=a1a2 ... aM andB=b1b2... bN is a list of ordered pairs, 〈(i1,j1), (i2j2), ..., (it,jtt)〉 such that ik < ik+1 and jk < jk+1. In this case the alignmentaligns symbols aik and bjk, and leaves blocks of unaligned symbols, orgaps, between them. A scoring schemeS associates costs for each aligned symbol pair and each gap. The alignment's score is the sum of the associated costs, and an optimal alignment is one of minimal score. There are a variety of schemes for scoring alignments. In a concave gap penalty scoring schemeS={δ, w}, a function δ(a, b) gives the score of each aligned pair of symbolsa andb, and aconcave function w(k) gives the score of a gap of lengthk. A function w is concave if and only if it has the property that, for allk > 1, w(k + 1) −w(k) ≤w(k) −w(k −1). In this paper we present an O(MP(logM + log2P)) algorithm for approximate regular expression matching for an arbitraryδ and any concavew.
45626993
Computable Boolean Algebras
Feiner [F] showed that a Boolean algebra need not have a computable copy (see also [T 2 ]). Downey and Jockusch [D-J] showed that every low Boolean algebra does have a computable copy. Thurber [T 3 ], showed that every low 2 Boolean algebra has a computable copy. Here we show that every Boolean algebra which is low 3 , or even low 4 , has a computable copy. The results of [D-J] and [T 3 ] were obtained by passing to linear orderings. In [D-J], there is an embedding theorem saying that any linear ordering which is with the successor relation as an added predicate can be embedded in a slightly larger linear ordering which is computable. An isomorphism theorem of Remmel [R] is used to show that the interval algebras of the two linear orderings are isomorphic (except in a trivial case). In [T3], there is an embedding theorem saying that any linear ordering which is with certain added predicates can be embedded in one which is with successor. Again the isomorphism theorem of Remmel is used to show that the interval algebras are isomorphic (except in a trivial case). Here, instead of passing to linear orderings, we work directly with Boolean algebras. We begin with a review of the known results. We re-formulate the embedding theorems of Downey-Jockusch and Thurber in terms of Boolean algebras. We extract from Remmel's isomorphism theorem some information on complexity. In this way, we show that a low Boolean algebra is isomorphic to a computable one by an isomorphism which is , at worst, and the same is true for a low 2 Boolean algebra.
4785970
Sequences of n-Diagrams
We consider only computable languages, and countable structures, with universe a subset of ω, which we think of as a set of constants. We identify sentences with their Gödel numbers. Thus, for a structure A, the complete (elementary) diagram, Dc(A), and the atomic diagram, D(A), are subsets of ω. We classify formulas as usual. A formula is both Σ0 and Π0 if it is open. For n > 0, a formula, in prenex normal form, is Σn, or Πn, if it has n blocks of like quantifiers, beginning with ∃, or ∀. For a formula θ, in prenex normal form, we let neg(θ) denote the dual formula that is logically equivalent to ¬θ–if θ is Σn, then neg(θ) is Πn, and vice versa.
8846958
Wearable computers and the possible development of musculoskeletal disorders
Work-related musculoskeletal disorders (WRMDs) have been shown to be caused by (amongst other things) exposure to work tasks which involve constrained pathomechanical body postures and physical load. Current research suggests that the added weight of a wearable computer and the positions which interacting with it requires, induces acute musculoskeletal stress and may lead to chronic musculoskeletal disorders. These disorders may only reveal themselves after a long period of time. Therefore it is important at this stage in wearable computer development to address these issues in the hope of diminishing their occurrence.