2,409 research outputs found
A Survey of Satisfiability Modulo Theory
Satisfiability modulo theory (SMT) consists in testing the satisfiability of
first-order formulas over linear integer or real arithmetic, or other theories.
In this survey, we explain the combination of propositional satisfiability and
decision procedures for conjunctions known as DPLL(T), and the alternative
"natural domain" approaches. We also cover quantifiers, Craig interpolants,
polynomial arithmetic, and how SMT solvers are used in automated software
analysis.Comment: Computer Algebra in Scientific Computing, Sep 2016, Bucharest,
Romania. 201
Analytic Tableaux for Simple Type Theory and its First-Order Fragment
We study simple type theory with primitive equality (STT) and its first-order
fragment EFO, which restricts equality and quantification to base types but
retains lambda abstraction and higher-order variables. As deductive system we
employ a cut-free tableau calculus. We consider completeness, compactness, and
existence of countable models. We prove these properties for STT with respect
to Henkin models and for EFO with respect to standard models. We also show that
the tableau system yields a decision procedure for three EFO fragments
The saturation conjecture (after A. Knutson and T. Tao)
In this exposition we give a simple and complete treatment of A. Knutson and
T. Tao's recent proof (http://front.math.ucdavis.edu/math.RT/9807160) of the
saturation conjecture, which asserts that the Littlewood-Richardson semigroup
is saturated. The main tool is Knutson and Tao's hive model for
Berenstein-Zelevinsky polytopes. In an appendix of W. Fulton it is shown that
the hive model is equivalent to the original Littlewood-Richardson rule.Comment: Latex document, 12 pages, 24 figure
Double transitivity of Galois Groups in Schubert Calculus of Grassmannians
We investigate double transitivity of Galois groups in the classical Schubert
calculus on Grassmannians. We show that all Schubert problems on Grassmannians
of 2- and 3-planes have doubly transitive Galois groups, as do all Schubert
problems involving only special Schubert conditions. We use these results to
give a new proof that Schubert problems on Grassmannians of 2-planes have
Galois groups that contain the alternating group. We also investigate the
Galois group of every Schubert problem on Gr(4,8), finding that each Galois
group either contains the alternating group or is an imprimitive permutation
group and therefore fails to be doubly transitive. These imprimitive examples
show that our results are the best possible general results on double
transitivity of Schubert problems.Comment: 25 page
Tableaux for the Logic of Strategically Knowing How
The logic of goal-directed knowing-how extends the standard epistemic logic
with an operator of knowing-how. The knowing-how operator is interpreted as
that there exists a strategy such that the agent knows that the strategy can
make sure that p. This paper presents a tableau procedure for the multi-agent
version of the logic of strategically knowing-how and shows the soundness and
completeness of this tableau procedure. This paper also shows that the
satisfiability problem of the logic can be decided in PSPACE.Comment: In Proceedings TARK 2023, arXiv:2307.0400
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