Non UBC
DSpace
Kolokolova, Antonina
2019-04-05T10:20:05Z
2018-08-30T17:04
The resolution proof system has been enormously helpful in deepening our
understanding of conflict-driven clause-learning (CDCL) SAT solvers. In the
interest of providing a similar proof complexity-theoretic analysis of
satisfiability modulo theories (SMT) solvers, we introduce a generalization
of resolution called Res(T). We show that many of the known results
comparing resolution and CDCL solvers lift to the SMT setting, such as the
result of Pipatsrisawat and Darwiche showing that CDCL solvers with
``perfect'' non-deterministic branching and an asserting clause-learning
scheme can polynomially simulate general resolution. We also describe a
stronger version of Res(T), Res*(T), capturing SMT solvers allowing
introduction of new literals.<br><br>
We analyze the theory EUF of equality with uninterpreted functions, and
show that the Res*(EUF) system is able to simulate an earlier calculus
introduced by Bjorner and De Moura for the purpose of analyzing DPLL(EUF).
Further, we show that Res*(EUF) (and thus SMT algorithms with clause
learning over EUF, new literal introduction rules and perfect branching)
can simulate the Frege proof system, which is well-known to be far more
powerful than resolution. Finally, we prove under the Exponential Time
Hypothesis (ETH) that any reduction from EUF to SAT (such as the Ackermann
reduction) must, in the worst case, produce an instance of size at least n
log n from an instance of size n.
https://circle.library.ubc.ca/rest/handle/2429/69478?expand=metadata
32.0
video/mp4
Author affiliation: Memorial University of Newfoundland
Oaxaca (Mexico : State)
10.14288/1.0377824
eng
Unreviewed
Vancouver : University of British Columbia Library
Banff International Research Station for Mathematical Innovation and Discovery
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
Faculty
BIRS Workshop Lecture Videos (Oaxaca (Mexico : State))
Mathematics
Computer science
Mathematical logic and foundations
Theoretical computer science
The Proof Complexity of SMT Solvers
Moving Image
http://hdl.handle.net/2429/69478