In this paper, we present a new image compression scheme, Projection-VQ, based on reconstruction from vector quantized projections. We can easily deal with the blocks of larger size in Projection-VQ than in conventional VQ schemes, because the dimension of vectors in projection domain is, in general, much smaller than that in the spatial domain. In Projection-VQ, the image can be reconstructed without destroying edge sharpness in the process since the projection data having the edge information are preferentially transmitted. There are several good algorithms of reconstructing an image from projections. However, we use a new modified reconstruction algorithm suitable for a variable bit rate image coding system. We allocate the bits depending on the characteristics of the block images. Our simulation results show that the performances are superior to the ordinary VQ schemes in PSNR, and that the improvement in subjective image quality is substantial.

Multiple context-free grammars (mcfg's) are a subclass of generalized context-free grammars introduced by Pollard in order to describe the syntax of natural languages. First, this paper shows that the universal recognition problem for mcfg's is EXP-POLY time-complete, where the universal recognition problem is the one to decide whether G generates w for a given grammar G and string w. Next, it is shown that the problem for linear context-free rewriting systems introduced by Vijay-Shanker et al., which is a proper subclass of mcfg's, is PSPACE-complete.

We review the role of optics in interconnects, analog processing, neural networks, and digital computing. The properties of low interference, massively parallel interconnections, and very high data rates promise extremely high performance for optical information processing systems.

There have been several studies related to a reduction of the amount of computational resources used by Turing machines. As consequences, Linear speed-up theorem", tape compression theorem" and reversal reduction theorem" have been obtained. In this paper, we discuss a leaf reduction theorem on alternating Turing machines. Recently, the result that one can reduce the number of leaves by a constant factor without increasing the space complexity was shown for space- and leaf-bounded alternating Turing machines. We show that for time- and leaf-bounded alternating Turing machines, the number of leaves can be reduced by a constant factor without increasing time used by the machine. Therefore, our result says that a constant factor on the leaf complexity does not affect the power of time- and leaf-bounded alternating Turing machines.

In this paper we study the problem of scheduling a tree-structured program on multiprocessors so as to minimize the total execution time, which includes communication delay between processors. It is assumed in the problem that a sufficiently large number of processors are available. It is known that if the program structures are restricted to be out-trees, the problem can be solved in O(n2) time, where n denotes the number of modules of a program. However, this problem is known to be NP-hard if the program structures are allowed to be in-trees. Up to now, no optimal algorithm, except an obvious one, was known for the latter case while some approximation algorithms were shown. We present an optimization algorithm with a nontrivial time bound O((1.52)nn log n) for the in-tree case.