51,957 research outputs found
ILP Modulo Data
The vast quantity of data generated and captured every day has led to a
pressing need for tools and processes to organize, analyze and interrelate this
data. Automated reasoning and optimization tools with inherent support for data
could enable advancements in a variety of contexts, from data-backed decision
making to data-intensive scientific research. To this end, we introduce a
decidable logic aimed at database analysis. Our logic extends quantifier-free
Linear Integer Arithmetic with operators from Relational Algebra, like
selection and cross product. We provide a scalable decision procedure that is
based on the BC(T) architecture for ILP Modulo Theories. Our decision procedure
makes use of database techniques. We also experimentally evaluate our approach,
and discuss potential applications.Comment: FMCAD 2014 final version plus proof
Joint Antenna Selection and Phase-Only Beamforming Using Mixed-Integer Nonlinear Programming
In this paper, we consider the problem of joint antenna selection and analog
beamformer design in downlink single-group multicast networks. Our objective is
to reduce the hardware costs by minimizing the number of required phase
shifters at the transmitter while fulfilling given distortion limits at the
receivers. We formulate the problem as an L0 minimization problem and devise a
novel branch-and-cut based algorithm to solve the resulting mixed-integer
nonlinear program to optimality. We also propose a suboptimal heuristic
algorithm to solve the above problem approximately with a low computational
complexity. Computational results illustrate that the solutions produced by the
proposed heuristic algorithm are optimal in most cases. The results also
indicate that the performance of the optimal methods can be significantly
improved by initializing with the result of the suboptimal method.Comment: to be presented at WSA 201
Foundations of Declarative Data Analysis Using Limit Datalog Programs
Motivated by applications in declarative data analysis, we study
---an extension of positive Datalog with
arithmetic functions over integers. This language is known to be undecidable,
so we propose two fragments. In
predicates are axiomatised to keep minimal/maximal numeric values, allowing us
to show that fact entailment is coNExpTime-complete in combined, and
coNP-complete in data complexity. Moreover, an additional
requirement causes the complexity to drop to ExpTime and PTime, respectively.
Finally, we show that stable can express many
useful data analysis tasks, and so our results provide a sound foundation for
the development of advanced information systems.Comment: 23 pages; full version of a paper accepted at IJCAI-17; v2 fixes some
typos and improves the acknowledgment
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
Solving Set Constraint Satisfaction Problems using ROBDDs
In this paper we present a new approach to modeling finite set domain
constraint problems using Reduced Ordered Binary Decision Diagrams (ROBDDs). We
show that it is possible to construct an efficient set domain propagator which
compactly represents many set domains and set constraints using ROBDDs. We
demonstrate that the ROBDD-based approach provides unprecedented flexibility in
modeling constraint satisfaction problems, leading to performance improvements.
We also show that the ROBDD-based modeling approach can be extended to the
modeling of integer and multiset constraint problems in a straightforward
manner. Since domain propagation is not always practical, we also show how to
incorporate less strict consistency notions into the ROBDD framework, such as
set bounds, cardinality bounds and lexicographic bounds consistency. Finally,
we present experimental results that demonstrate the ROBDD-based solver
performs better than various more conventional constraint solvers on several
standard set constraint problems
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