Algorithms for computing congruence closure of ground equations over uninterpreted symbols and interpreted satisfying associativity commutativity (AC) properties are proposed. The algorithms based on a framework by abstracting nonflat terms constants as proposed first in Kapur's algorithm (RTA97). is general, flexible, has been extended also to develop the cases when associative-commutative fun...

An n-ary operation f : An → A is called cyclic, if it is idempotent and f(a1, a2, a3, . . . , an) = f(a2, a3, . . . , an, a1) for every a1, . . . , an ∈ A. We prove that every finite algebra A in a congruence modular variety has a p-ary cyclic term operation for any prime p greater than |A|.

Software projects are frequently distributed across multiple sites. While this practice takes advantage of local expertise and differential cost structures, there is a hidden coordination cost. Modularity and even agile methods have had mixed success in addressing distributed development. Recent studies on congruence provide a new way to understand coordination on software projects. We used a v...

In the situation of shortened product life cycles, modular product design enables organizations to adapt to unanticipated changes in their environments. This study extends modular systems theory to manufacturing process design and posits that: (i) firms can design their manufacturing processes for the same product into either an integrated or modularized structure, thereby being agile in dynami...

In this paper the question is considered in which cases a transition system specification in Plotkin style has 'good' properties and deserves the predicate 'structured'. The discussion takes place in a setting of labelled transition systems. The states of the transition systems are terms generated by a single sorted signature and the transitions between states are defined by conditional rules. ...

The study of modular forms for congruence subgroups of SL2(Z) has been one of the central topics in number theory for over one century. It has broad applications and impact to many branches of mathematics. Langlands’ program is a vast generalization of this subject from representation-theoretic point of view. The most recent highlight is the proof of the Taniyama-Shimura-Weil modularity conject...

Detecting communities plays a vital role in studying group level patterns of a social network and it can be helpful in developing several recommendation systems such as movie recommendation, book recommendation, friend recommendation and so on. Most of the community detection algorithms can detect disjoint communities only, but in the real time scenario, a node can be a member of more than one ...