It is generally assumed that hashing is essential to solve many language processing problems efficiently; e.g., symbol table formation and maintenance, grammar manipulation, basic block optimization, and global optimization. This paper questions this assumption, and initiates development of an efficient alternative compiler methodology without hashing or sorting. The methodology rests on effici...

In this paper, we introduce a new paradigm multiset-based tree model. We show that trees can be represented in the form of wellfounded multisets. We also show that the conventional approach for this representation is not injective from a set of trees to the class of multisets representing such trees. We establish a oneto-one correspondence between trees and suitable permutations of a wellfounde...

A permutation σ of a multiset is called Stirling permutation if σ(s) ≥ σ(i) as soon as σ(i) = σ(j) and i < s < j. In our paper we study Stirling polynomials that arise in the generating function for descent statistics on Stirling permutations of any multiset. We develop generalizations of the classical Stirling numbers and present their combinatorial interpretations. Particularly, we apply the ...

We introduce a computing mechanism of a biochemical inspiration (similar to a P system in the area of computing by membranes) which consists of a multiset of symbol-objects and a set of nite state sequential transducers. The transducers process symbols in the current multiset in the usual manner. A computation starts in an initial con guration and ends in halting con guration. The power of thes...

Let F be a finite field. A multiset S of integers is projectionforcing if for every linear function φ : F → F whose multiset of weight changes is S, φ is a coordinate projection up to permutation of entries. The MacWilliams Extension Theorem from coding theory says that S = {0, 0, . . . , 0} is projection-forcing. We give a (super-polynomial) algorithm to determine whether or not a given S is p...

In an anonymous ring of n processors, all processors are totally indistinguishable except for their input values. These values are not necessarily distinct, i.e., they form a multiset, and this makes many problems particularly difficult. We consider the problem of distributively sorting such a multiset on the ring, and we give a complete characterization of the relationship with the problems of...

This paper presents a mechanism for developing distributed learners for learning production rules from massive, dynamic, and distributed databases. The task of distributed learning is formulated by the concept of multiset decision tables that is based on rough multisets and information multisystems, which are derived from the theory of rough sets. We use the concept of partition of boundary set...

This paper introduces the concept of a single valued neutrosophic multiset (SVNM) as a generalization of an intuitionistic fuzzy multiset (IFM) and some basic operational relations of SVNMs, and then proposes the Dice similarity measure and the weighted Dice similarity measure for SVNMs and investigates their properties. Finally, the Dice similarity measure is applied to a medical diagnosis pro...

We study the problem of existence of (nontrivial) perfect codes in the discrete n-simplex ∆` := {( x0, . . . , xn ) : xi ∈ Z+, ∑ i xi = ` } under `1 metric. The problem is motivated by the so-called multiset codes, which have recently been introduced by the authors as appropriate constructs for error correction in the permutation channels. It is shown that e-perfect codes in the 1-simplex ∆` ex...

We consider the problem of reconstructing a set of real numbers up to translation from the multiset of its subsets of fixed size, given up to translation. This is impossible in general: for instance almost all subsets of Z contain infinitely many translates of every finite subset of Z. We therefore restrict our attention to subsets of R which are locally finite; those which contain only finitel...