Daniel P. Bovet

A uniform approach to define complexity classes

Abstract Complexity classes are usually defined by referring to computation models and by putting suitable restrictions on them. Following this approach, many proofs of results are tightly bound to the characteristics of the computation model and of its restrictions and, therefore, they sometimes hide the essential properties which insure the obtained results. In order to obtain more general results, a uniform family of computation models which encompasses most of the complexity classes of interest is introduced. As a first initial set of results derivable from the proposed approach, we will give a sufficient and necessary condition for proving separations of relativized complexity classes, a characterization of complexity classes with complete languages and a sufficient condition for proving strong separations of relativized complexity classes. Examples of applications of these results to some specific complexity classes are then given. Additional results related to separations by sparse oracles can be found in Bovet (1991).

On the regularity of languages on a binary alphabet generated by copying systems

Abstract Let A be a binary alphabet and ⊢∗π the derivation relation associated to the semi-Thue system π={(x, xx)∣x ∈A ∗ } . We prove that ⊢∗π is a well quasi order in A∗. As a consequence of this we show that the languages which are upwards closed with respect to ⊢∗π are all regular.

Minimum-delay schedules in layered networks

SummaryIn this paper, we consider the following problem: given a layered network including a set of messages, each of which must be transmitted from a source to a sink node, what is the sequence of moves from one node to another which minimizes the total completion time? We first show that the general problem is NP-complete for both fixed and variable path routing (thus the scheduling problem for more realistic networks with cycles must be considered computationally intractable). We then consider several restrictions which admit polynomia time algorithms.

Minimal deadlock-free store-and-forward communication networks

Store-and-forward communication networks may be designed so as to be free from store-and-forward deadlock. This is accomplished by incorporating in the network an acyclic buffer graph on which messages are forwarded, from buffer to buffer, according to all the desired routes. A technique producing minimum buffer graphs for a rather large class of networks is illustrated. Successively, a comparison is made with other well-known deadlock avoidance techniques, showing that substantial savings can be achieved.

DEADLOCK PREDICTION IN THE CASE OF DYNAMIC ROUTING

One of the main issues in flow control problems is deadlock of messages caused by a limited amount of resources. In this paper, the problem of predicting whether a deadlock will necessarily occur in a Store-and-Forward Network is analyzed. We show that, in the case of dynamic routing, the deadlock prediction problem can be decided in polynomial time if tokens are allowed to transit more than once through the same vertex, in contrast with an NP-completeness result in the case where they are allowed to transit at most once.

On the Number of Switching Modes Generated by Time-Optimal Algorithms for SS/TDMA Systems

An important parameter related to the efficiency of algorithms for data transmission on SS/TDMA systems is the number of switching modes they generate. It is shown in this note that time-optimal algorithms produce the maximum number of switchings only if the transmission duration L is exponential in N , where N is the number of channels. This result explains the good performance exhibited by those algorithms in several simulation results.