计数辅助下推自动机和半无界算术电路

[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI:10.1109/SCT.1991.160269

V. Vinay

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引用次数: 127

摘要

研究了空间有界不确定性辅助下推机上的各种计数方法。在主要定理中，展示了如何通过统一的布尔电路族有效地模拟NAuxPDA，这些电路族保持NAuxPDA中接受路径的数量作为布尔电路中接受子树的数量。所使用的技术通过考虑AuxPDA的高度和反转边界，以一种新颖的方式模拟NAuxPDA。本文工作的重点之一是对重要类DET的精确描述。结果表明，DET正是可以用两台计数对数空间机器的输出差来计算的函数类。

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Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits

The author examines various counting measures on space bounded nondeterministic auxiliary pushdown machines. In the main theorem, it is shown how a NAuxPDA may be simulated efficiently by a uniform family of Boolean circuits, which preserve the number of accepting paths in the NAuxPDA as the number of accepting subtrees in the Boolean circuit. The techniques used simulate the NAuxPDA in a novel way by considering the height and reversal bounds of an AuxPDA. One of the highlights of the present work is an exact characterization of the important class DET. It is shown that DET is exactly the class of functions that can be computed as the difference between the outputs of two counting logspace machines.<>

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[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference

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