Connections between circuit analysis problems and circuit lower bounds
Author(s)
Murray, Cody (Cody Daniel)
DownloadFull printable version (7.536Mb)
Other Contributors
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Advisor
Ryan Williams.
Terms of use
Metadata
Show full item recordAbstract
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.
Description
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).
Date issued
2018Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer SciencePublisher
Massachusetts Institute of Technology
Keywords
Electrical Engineering and Computer Science.