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Electronic Colloquium on Computational Complexity

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All reports by Author Ian Mertz:

TR23-179 | 18th November 2023
Ian Mertz

Reusing Space: Techniques and Open Problems

In the world of space-bounded complexity, there is a strain of results showing that space can, somewhat paradoxically, be used for multiple purposes at once. Touchstone results include Barrington’s Theorem and the recent line of work on catalytic computing. We refer to such techniques, in contrast to the usual notion ... more >>>

TR23-174 | 15th November 2023
James Cook, Ian Mertz

Tree Evaluation is in Space O(log n · log log n)

The Tree Evaluation Problem ($TreeEval$) (Cook et al. 2009) is a central candidate for separating polynomial time ($P$) from logarithmic space ($L$) via composition. While space lower bounds of $\Omega(\log^2 n)$ are known for multiple restricted models, it was recently shown by Cook and Mertz (2020) that TreeEval can be ... more >>>

TR15-018 | 31st January 2015
Eric Allender, Ian Mertz

Complexity of Regular Functions

Revisions: 1

We give complexity bounds for various classes of functions computed by cost register automata.

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TR14-122 | 30th September 2014
Eric Allender, Anna Gal, Ian Mertz

Dual VP Classes

Revisions: 2

We consider arithmetic complexity classes that are in some sense dual to the classes VP(Fp) that were introduced by Valiant. This provides new characterizations of the complexity classes ACC^1 and TC^1, and also provides a compelling example of
a class of high-degree polynomials that can be simulated via arithmetic circuits ... more >>>

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