Some problems in speech and natural language processing involve combining two information sources each modeled by a stochastic context-free grammar. Such cases include parsing the output of a speech recognizer by using a contextfree language model, finding the best solution among all the possible ones in language generation, preserving ambiguity in machine translation. In these cases usually at...

We study a two-point free boundary problem for a quasilinear parabolic equation. This problem arises in the model of flame propagation in combustion theory. It also arises in the study of the motion of interface moving with curvature in which the studied problem is confined in the conical region bounded by two straight lines and the interface has prescribed touching angles with these two straig...

The naturalistic voluntary control (VC) theory explains free will and consciousness in terms of each other. It is central to free voluntary control of action that one can control both what one is conscious of, and also what one is not conscious of. Furthermore, the specific cognitive ability or skill involved in voluntarily controlling whether information is processed consciously or unconscious...

A bidimensional bifix (in short bibifix ) of a square matrix T is a square submatrix of T which occurs in the top-left and bottomright corners of T . This allows us to extend the definition of bifix-free words and cross-bifix-free set of words to bidimensional structures. In this paper we exhaustively generate all the bibifix -free square matrices and we construct a particular non-expandable cr...

In the two-sided pushdown automata discussed in this paper, their two-sided pushdowns are introduced over free groups rather than free monoids. It is demonstrated that these automata with pushdowns introduced in this way characterize the family of recursively enumerable languages.

ABSTRACT. The key result in the paper concerns two transformations, Φ : (ρ, ψ) 7→ φ and Bt : ψ 7→ φ, where ρ, ψ, φ are states on the algebra of non-commutative polynomials, or equivalently joint distributions of d-tuples of non-commuting operators. These transformations are related to free probability: if ⊞ is the free convolution operation, and {ρt} is a free convolution semigroup, we show tha...

We consider the problem of fair division of a two dimensional heterogeneous good among several agents. Applications include division of land as well as ad space in print and electronic media. Classical cake cutting protocols either consider a one-dimensional resource, or allocate each agent several disconnected pieces. In practice, however, the two dimensional shape of the allotted piece is of ...

The growth of the internet provides opportunities for cooperative computation, it also requires development of protocols that can accomplish this task among mutually untrusting parties. The aim is to develop methods which ensure both the correct evaluation of the function and privacy of individual inputs. Multiparty Computation protocols help to achieve the aim without using a trusted third par...

Conjugacy classes of primitive words in the free group of rank two can indexed by the rationals. A representative for each conjugacy class is given by a recursive enumeration scheme and the representative, usually called a Farey word, is denoted by Wp/q where p and q are relatively prime integers. Primitive pairs, that is, pairs of words that generate the free group, correspond to pairs of word...