A graph based parsing algorithm for context-free languages

We present a simple algorithm deciding the word problem of c. f. languages in O(n^{3}). It decides this problem in time O(n^{2}) for unambiguous grammars and in time O(n) in the case of LR(k) grammars

Analytic machines

In this paper we present some results about it analytic machines regarding th power of computations over sf bf Q and sf bf R, solutions of differential equations and the stability problem of dynamical systems. We first explain the machine model, wich is a kind of sc Blum-Shub-Smale machine enhanced by infinite convergent computiations. Next, we compare the computional power of such machinesofer the fields sf bf Q and sf bf R showing that finite computations with real numbers can be simulated by infinite converging computations on rational numbers, but the precision of the approximation is not known during the process. Our attention is then shifted to it ordinary differential equations (ODEs), dynamical systems described by ODEs and the undecidability of a class of stability problems for dynamical syste

Designing correct recursive circuits using semantics-preserving transformations of nets

This paper will present a method of formal synthesis to design correct recursive circuits by using semantics-preserving transformations of nets (SPTNs). Its theoretical base is an algebraic calculus of nets. The calculus of nets is a hardware-specific calculus, and the transformations are circuit transformations themselves. Thus, it is much better adapted to the synthesis domain. The start point of the method is a conceptually simple specification for the required function. This specification can be easily proved to be correct, thereby the perplexed problem of the specification validation can be avoided. The specification is described compactly and graphically by a small kernel of recursive equations, and the synthesis task is simplified to transform these recursive equations in in the kernel. Because only semantics-preserving transformations are allowed in synthesis procedures, the synthesis result is not only a hardware implementation, but also a proof of correctness. We will illustrate two ways to transform a basic sorter into a odd-even-merging sorter, one being based on local incremantal transformations and the other being based on global partitions. The results show that there are circuits of practical interest, which can derived formally by using this method

Ein logisch-topologischer Kalkül zur Konstruktion von integrierten Schaltkreisen

Es wird ein CAD-System ICAD-IC vorgestellt, das den Entwurf integrierter Schaltungen unterstützen soll. Der Kern des Systems besteht in einem Netzkalkül, der es erlaubt, neben der logischen Information auch geometrische Informationen zu handhaben. Dieser Kalkül besitzt verschiedene Ausprägungen, die den Entwurf auf verschiedenen Entwurfsebenen unterstützen. Das System ist um den Kalkül herum entwickelt, wie etwa ALGOL um die Numerik. Soweit das System bis jetzt entwickelt ist, betrifft es die logisch-topologische Entwurfsebene und den Übergang zur topographischen Entwurfsebene. Wir stellen hier das Konzept des Kalküls vor und erläutern an Beispielen einige Grundlagenuntersuchungen zu diesem Thema.We present a CAD-system \u27CAD-IC\u27, supporting the automatic design of integrated circuits. The kernel of the system is based on a "calculus of nets", which allows both, the handling of logical and geometrical information. Depending on the design-level different versions of this calculus may be adopted. The system itself is built around this calculus, as f.e. ALGOL around numerics. As far as the system is developed at the moment, it mainly deals with the logical-topological design level and the transition to the topographical level. We give the main ideas of the calculus and illustrate some basic investigations with help of examples