On quaternary associative operations

Smooth associative operations on finite chains

Broadcast and Associative Operations on Fat-Trees

This paper analyzes the cost of performing broadcast, product and prefix computation on the ideal fat-tree, a model proposed here to capture distance and bandwidth properties common to a variety of fat-tree networks. Algorithms are developed and analyzed in terms of the capacity of channels at different levels of the fat-tree. Non trivial lower bounds are derived establishing the optimality of ...

Non-Associative Operations

Abstract: How is fuzzy logic usually formalized? There are many seemingly reasonable requirements that a logic should satisfy: e.g., since and are the same, the corresponding and-operation should be commutative. Similarly, since means the same as , we should expect that the and-operation should also satisfy this property, etc. It turns out to be impossible to satisfy all these seemingly natural...

ASSOCIATIVE REGULAR OPERATIONS ON GROUPS CORRESPONDING TO A PROPERTY <p

In previous papers [4; 5; 6] we constructed and studied many classes of operations on groups which have the following properties: (1) Associative; (2) Commutative; (3) The resultant group contains isomorphic images of the original factors and is generated by them; (4) In the resultant group the intersection of a factor with normal subgroup generated by the remaining factors is the unit element....

Almost Associative Operations Generating a Minimal Clone

Characterizations of ‘almost associative’ binary operations generating a minimal clone are given for two interpretations of the term ‘almost associative’. One of them uses the associative spectrum, the other one uses the index of nonassociativity to measure how far an operation is from being associative.