This paper explores the language classes that arise with respect to the head count of a finite ultrametric automaton. First we prove that in the one-way setting there is a language that can be recognized by a one-head ultrametric finite automaton and cannot be recognized by any k-head non-deterministic finite automaton. Then we prove that in the two-way setting the class of languages recognized...

In [6] it was shown that shuffle languages are contained in one-way-NSPACE(log n) and in P. In this paper we show that nondeterministic one-way logarithmic space is in some sense the lower bound for accepting shuffle languages. Namely, we show that there exists a shuffle language which is not accepted by any deterministic one-way Turing machine with space bounded by a sublinear function, and th...

In this paper, we propose several deadlock-free protocols for implementing the generalized alternative construct, where a process non-deterministically chooses between sending or receiving among various synchronous channels. We consider general many-to-many channels and examine in detail the special case of fan (many-toone and one-to-many) channels, which are common and can be implemented much ...

We examine the succinctness of one-way, rotating, sweeping, and two-way deterministic finite automata (1dfas, rdfas, sdfas, 2dfas) and their nondeterministic and randomized counterparts. Here, a sdfa is a 2dfa whose head can change direction only on the endmarkers and a rdfa is a sdfa whose head is reset to the left end of the input every time the right end-marker is read. We study the size com...

A sweeping automaton is a two-way deterministic finite automaton which makes turns only at the endmarkers. Sipser [12] has proved that one-way nondeterministic finite automata can be exponentially more succinct in sizes than sweeping automata. In this paper, we propose a technique based on the work in [6] for establishing lower bounds on the size of sweeping automata. We show that Sipser’s tech...

We derive a deterministic particle method for the solution of nonlinear reactiondiffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of ...

Consider the following simple communication problem. Fix a universe U and a family Ω of subsets of U . Players I and II receive, respectively, an element a ∈ U and a subset A ∈ Ω. Their task is to find a subset B of U such that |A∩B| is even and a ∈ B. With every Boolean function f we associate a collection Ωf of subsets of U = f−1(0), and prove that its (one round) communication complexity com...