It is known that the weakly monotone restarting automata acceptexactly the growing context-sensitive languages. We introduce ameasure on the degree of weak monotonicity and show that thelanguage classes obtained in this way form strict hierarchies forthe various types of deterministic and nondeterministic restartingautomata without auxiliary symbols.

We study the properties of the function R(n) which determines the number of representationsof an integer n as a sum of distinct Fibonacci numbers F k . We determine the maximum andmean values of R(n) for Fk ≤ n < Fk+1 .

Among several alternative viewpoints for building software quality metrics, evaluating the consistency between different modelsin a software specification or implementation appears to be fruitful.An obvious difficulty is that different models are usually expressedby means of different concepts, and then, confronting heterogeneousrepresentations is not straightforward.In this paper, we propose a solution for measuring theconsistency between the architecture and the communication models.After some sensible transformations, the information about bothmodels are captured trough hierarchical representations. We defineand discuss a similarity measure between hierarchies, that eventuallyfounds the software metric we propose. Lastly, we investigate how toscale and interpret the metric values and give an application examplewith SDL.

Resolving an open problem of Ravikumar and Quan, we show that equivalence of prefix grammars is complete in PSPACE. We also showthat membership for these grammars is complete in P (it was known that this problem is in P) and characterize thecomplexity of equivalence and inclusion for monotonic grammars. For grammars with several premises we show that membershipis complete in EXPTIME and hard for PSPACE for monotonicgrammars.

We consider systems consisting of finite automata communicating by exchanging messagesand working on the same read-only data.We investigate the situation in which the automata work with constantbut different speeds. We assume furthermore that the automata are not aware of the speeds andthey cannot measure them directly. Nevertheless, the automata have to compute a correct output. We call this model multi-speed systems of finite automata.Complexity measure that we consider here is the number of messages sent by the automata.The main result of this paper is that multi-speed systems are as powerful as synchronous systems, in whichall automata work with the same speed.