Pierre McKenzie

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We prove tight lower bounds, of up to n , for the monotone depth of functions in monotone-P. As a result we achieve the separation of the following classes. 1. monotone-NC 6 = monotone-P. 2. For every i 1, monotone-NC i 6 = monotone-NC i+1. 3. More generally: For any integer function D(n), up to n (for some > 0), we give an explicit example of a monotone(More)
This paper describes the simulation of an S(n) spacebounded deterministic Turing machine by a reversible Turing machine operating in space S(n). It thus answers a question posed by Bennett in 1989 and refutes the conjecture, made by Li and Vitanyi in 1996, that any reversible simulation of an irreversible computation must obey Bennett’s reversible pebble(More)
The problem of testing membership in the subset of the natural numbers produced at the output gate of a { $$\bigcup, \bigcap, ^-, +, \times$$ } combinational circuit is shown to capture a wide range of complexity classes. Although the general problem remains open, the case { $$\bigcup, \bigcap, +, \times$$ } is shown NEXPTIME-complete, the cases {(More)
The computation tree of a nondeterministic machine M with input x gives rise to a leaf string formed by concatenating the outcomes of all the computations in the tree in lexicographical order. We may characterize problems by considering, for a particular \leaf language" Y , the set of all x for which the leaf string of M is contained in Y . In this way, in(More)
We deene the counting classes #NC 1 , GapNC 1 , PNC 1 and C = NC 1. We prove that boolean circuits, algebraic circuits, programs over non-deterministic nite automata, and programs over constant integer matrices yield equivalent deenitions of the latter three classes. We investigate closure properties. We observe that #NC 1 #L, that PNC 1 L, and that C = NC(More)
Known to be decidable since 1981, there still remains a huge gap between the best known lower and upper bounds for the reach ability problem for vector addition systems with states (VASS). Here the problem is shown PSPACE-complete in the two-dimensional case, vastly improving on the doubly exponential time bound established in 1986 by Howell, Rosier, Huynh(More)
We introduce the <i>tree evaluation problem</i>, show that it is in <b>LogDCFL</b> (and hence in <b>P</b>), and study its branching program complexity in the hope of eventually proving a superlogarithmic space lower bound. The input to the problem is a rooted, balanced <i>d</i>-ary tree of height <i>h</i>, whose internal nodes are labeled with <i>d</i>-ary(More)