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Electronic Colloquium on Computational Complexity

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Reports tagged with Catalytic Computation:
TR19-095 | 18th July 2019
Chetan Gupta, Rahul Jain, Vimal Raj Sharma, Raghunath Tewari

Unambiguous Catalytic Computation

The catalytic Turing machine is a model of computation defined by Buhrman, Cleve,
Kouck, Loff, and Speelman (STOC 2014). Compared to the classical space-bounded Turing
machine, this model has an extra space which is filled with arbitrary content in addition
to the clean space. In such a model we study ... more >>>

TR20-024 | 20th February 2020
Samir Datta, Chetan Gupta, Rahul Jain, Vimal Raj Sharma, Raghunath Tewari

Randomized and Symmetric Catalytic Computation

A catalytic Turing machine is a model of computation that is created by equipping a Turing machine with an additional auxiliary tape which is initially filled with arbitrary content; the machine can read or write on auxiliary tape during the computation but when it halts auxiliary tape’s initial content must ... more >>>

TR20-056 | 17th April 2020
James Cook, Ian Mertz

Catalytic Approaches to the Tree Evaluation Problem

The study of branching programs for the Tree Evaluation Problem, introduced by S. Cook et al. (TOCT 2012), remains one of the most promising approaches to separating L from P. Given a label in $[k]$ at each leaf of a complete binary tree and an explicit function in $[k]^2 \to ... more >>>

TR21-035 | 13th March 2021
Robert Robere, Jeroen Zuiddam

Amortized Circuit Complexity, Formal Complexity Measures, and Catalytic Algorithms

Revisions: 1

We study the amortized circuit complexity of boolean functions.

Given a circuit model $\mathcal{F}$ and a boolean function $f : \{0,1\}^n \rightarrow \{0,1\}$, the $\mathcal{F}$-amortized circuit complexity is defined to be the size of the smallest circuit that outputs $m$ copies of $f$ (evaluated on the same input), ... more >>>

TR21-054 | 14th April 2021
James Cook, Ian Mertz

Encodings and the Tree Evaluation Problem

We show that the Tree Evaluation Problem with alphabet size $k$ and height $h$ can be solved by branching programs of size $k^{O(h/\log h)} + 2^{O(h)}$. This answers a longstanding challenge of Cook et al. (2009) and gives the first general upper bound since the problem's inception.

more >>>

TR22-026 | 17th February 2022
James Cook, Ian Mertz

Trading Time and Space in Catalytic Branching Programs

An $m$-catalytic branching program (Girard, Koucky, McKenzie 2015) is a set of $m$ distinct branching programs for $f$ which are permitted to share internal (i.e. non-source non-sink) nodes. While originally introduced as a non-uniform analogue to catalytic space, this also gives a natural notion of amortized non-uniform space complexity for ... more >>>

TR23-036 | 27th March 2023
Dean Doron, Roei Tell

Derandomization with Minimal Memory Footprint

Existing proofs that deduce BPL=L from circuit lower bounds convert randomized algorithms into deterministic algorithms with large constant overhead in space. We study space-bounded derandomization with minimal footprint, and ask what is the minimal possible space overhead for derandomization.
We show that $BPSPACE[S] \subseteq DSPACE[c \cdot S]$ for $c \approx ... more >>>

TR23-168 | 13th November 2023
Edward Pyne

Time-Space Tradeoffs for BPL via Catalytic Computation

Revisions: 1

We prove that for every $\alpha \in [1,1.5]$,
\text{BPSPACE}[S]\subseteq \text{TISP}[2^{S^{\alpha}},S^{3-\alpha}]
where $\text{BPSPACE}[S]$ corresponds to randomized space $O(S)$ computation, and $\text{TISP}[T,S]$ to time $poly(T)$, space $O(S)$ computation. Our result smoothly interpolates between the results of (Nisan STOC 1992) and (Saks and Zhou FOCS 1995), which prove $\text{BPSPACE}[S]$ is contained ... 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 >>>

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 >>>

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