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The previous are identical to the expressions (2) and (3). Thus the n 1 columns do consist of two repetitions of 2”-r-level Gray code. Now if we combine the first two columns again, we reduce each 2”-‘-level Gray code into two 2n-2-level Gray codes, or, the complete array into four 2”-2-level Gray codes. This can continue until we have only m columns, which(More)
The field of machine translation is almost as old as the modern digital computer. In 1949 Warren Weaver suggested that the problem be attacked with statistical methods and ideas from information theory, an area which he, Claude Shannon, and others were developing at the time (Weaver 1949). Although researchers quickly abandoned this approach, advancing(More)
-Register allocation may be viewed as a graph coloring problem. Each node in the graph stands for a computed quantity that resides in a machine register, and two nodes are connected by an edge if the quantities interfere with each other, that is, if they are simultaneously live at some point in the object program. This approach, though mentioned in the(More)
An approach to automatic translation is outlined that utilizes technklues of statistical inl 'ormatiml extraction from large data bases. The method is based on the availability of pairs of large corresponding texts that are translations of each other. In our case, the iexts are in English and French. Fundamenta l to the technique is a complex glossary of(More)
The global data relationships in a program can be exposed and codified by the static analysis methods described in this paper. A procedure is given which determines all the definitions which can possibly “reach” each node of the control flow graph of the program and all the definitions that are “live” on each edge of the graph. The(More)
When considering compiler optimization, there are two questions that immediately come to mind; one, why and to what extent is optimization necessary and two, to what extent is it possible. When considering the second question, one might immediately become discouraged since it is well known that the program equivalency problem is recursively unsolvable. It(More)
By a simple direct construction it is shown that computations done by Turing machines can be duplicated by a very simple symbol manipulation process. The process is described by a simple form of Post canonical system with some very strong restrictions. This system is <italic>monogenic</italic>: each formula (string of symbols) of the system can be affected(More)