It is known that a queue is not finitely definable in ACP with handshaking communication (Baeten and Berg&a, 1988). In this paper, two finite specifications of a queue in ACP with abstraction and handshaking are proved correct relative to a standard specification of a queue that employs an infinite data type for representing its contents. The proofs are given in the proof theory of &RL, and the...

Abstract. We prove several results regarding some invariants of elliptic curves on average over the family of all elliptic curves inside a box of sides A and B. As an example, let E be an elliptic curve defined over Q and p be a prime of good reduction for E. Let eE (p) be the exponent of the group of rational points of the reduction modulo p of E over the finite field Fp. Let C be the family o...

Abstract There has been recent interest in a hybrid form of the celebrated conjectures Hardy–Littlewood and Chowla. We prove that for any $k,\ell \ge 1$ distinct integers $h_2,\ldots ,h_k,a_1,\ldots ,a_\ell $ , we have: $$ \begin{align*}\sum_{n\leq X}\mu(n+h_1)\cdots \mu(n+h_k)\Lambda(n+a_1)\cdots\Lambda(n+a_{\ell})=o(X)\end{align*} all except $o(H)$ values $h_1\leq H$ so long as $H\geq (\log X...

We use the quasi-ordering of substructure relations such as induced and weak subgraph, induced suborder, graph minor or subformula of a CNF formula to obtain recognition algorithms for hereditary properties that are fast on average. The ingredients needed besides inheritance are independence of the occurrence of small substructures in a random input and the existence of algorithms for recogniti...

We prove a direct sum theorem for randomized communication complexity. Ignoring logarithmic factors, our results show that: • Computing n copies of a function requires √n times the communication. • For average case complexity, given any distribution μ on inputs, computing n copies of the function on n independent inputs sampled according to μ requires √ n times the communication for computing o...