2026-09-18T20:30:36Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1204672026-06-16T18:15:37Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Ryan Williams.
Murray, Cody (Cody Daniel)
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2019-02-15T19:36:39Z
2019-02-15T19:36:39Z
2018
2018
http://hdl.handle.net/1721.1/120467
1084478697
Thesis: Ph. D. in Computer Science and Engineering, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 107-112).
A circuit analysis problem takes a Boolean function f as input (where f is represented either as a logical circuit, or as a truth table) and determines some interesting property of f. Examples of circuit analysis problems include Circuit Satisfiability, Circuit Composition, and the Minimum Size Circuit Problem (MCSP). A circuit lower bound presents an interesting function f and shows that no "easy" family of logical circuits can compute f correctly on all inputs, for some definition of "easy". Lower bounds are infamously hard to prove, but are of significant interest for understanding computation. In this thesis, we derive new connections between circuit analysis problems and circuit lower bounds, to prove new lower bounds for various well-studied circuit classes. We show how faster algorithms for Circuit Satisfiability can imply non-uniform lower bounds for functions in NP and related classes. We prove that MCSP cannot be NP-hard under "local" gadget reductions of the kind that appear in textbooks, and if MCSP proved to be NP-hard in the usual (polynomial-time reduction) sense then we would also prove longstanding lower bounds in other regimes. We also prove that natural versions of the Circuit Composition problem do not have small circuits that are constructible in very small (logarithmic) space.
by Cody Murray.
Ph.D. in Computer Science and Engineering
112 pages
eng
Massachusetts Institute of Technology
MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.
http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
Connections between circuit analysis problems and circuit lower bounds
Thesis
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<Abstract>A circuit analysis problem takes a Boolean function f as input (where f is represented either as a logical circuit, or as a truth table) and determines some interesting property of f. Examples of circuit analysis problems include Circuit Satisfiability, Circuit Composition, and the Minimum Size Circuit Problem (MCSP). A circuit lower bound presents an interesting function f and shows that no "easy" family of logical circuits can compute f correctly on all inputs, for some definition of "easy". Lower bounds are infamously hard to prove, but are of significant interest for understanding computation. In this thesis, we derive new connections between circuit analysis problems and circuit lower bounds, to prove new lower bounds for various well-studied circuit classes. We show how faster algorithms for Circuit Satisfiability can imply non-uniform lower bounds for functions in NP and related classes. We prove that MCSP cannot be NP-hard under "local" gadget reductions of the kind that appear in textbooks, and if MCSP proved to be NP-hard in the usual (polynomial-time reduction) sense then we would also prove longstanding lower bounds in other regimes. We also prove that natural versions of the Circuit Composition problem do not have small circuits that are constructible in very small (logarithmic) space.</Abstract>
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