相关论文: Deciding Quantifier-Free Presburger Formulas Using…
All known quantifier elimination procedures for Presburger arithmetic require doubly exponential time for eliminating a single block of existentially quantified variables. It has even been claimed in the literature that this upper bound is…
We give a quantifier elimination procedure for one-parametric Presburger arithmetic, the extension of Presburger arithmetic with the function $x \mapsto t \cdot x$, where $t$ is a fixed free variable ranging over the integers. This resolves…
Automata provide a decision procedure for Presburger arithmetic. However, until now only crude lower and upper bounds were known on the sizes of the automata produced by this approach. In this paper, we prove an upper bound on the the…
We give a quantifier elimination procedures for the extension of Presburger arithmetic with a unary threshold counting quantifier $\exists^{\ge c} y$ that determines whether the number of different $y$ satisfying some formula is at least $c…
We study VC-dimension of short formulas in Presburger Arithmetic, defined to have a bounded number of variables, quantifiers and atoms. We give both lower and upper bounds, which are tight up to a polynomial factor in the bit length of the…
We identify a fragment of Presburger arithmetic enriched with free function symbols and cardinality constraints for interpreted sets, which is amenable to automated analysis. We establish decidability and complexity results for such a…
We present a first-order theory of sequences with integer elements, Presburger arithmetic, and regular constraints, which can model significant properties of data structures such as arrays and lists. We give a decision procedure for the…
In this paper, we consider the satisfiability problem for string logic with equations, regular membership and Presburger constraints over length functions. The difficulty comes from multiple occurrences of string variables making…
Many real applications problems can be encoded easily as quantified formulas in SMT. However, this simplicity comes at the cost of difficulty during solving by SMT solvers. Different strategies and quantifier instantiation techniques have…
The decision boundaries of Bayes classifier are optimal because they lead to maximum probability of correct decision. It means if we knew the prior probabilities and the class-conditional densities, we could design a classifier which gives…
We generalize Cooper's method of quantifier elimination for classical Presburger arithmetic to give a new proof that all parametric Presburger families (as defined by Kevin Woods) are definable by formulas with polynomially bounded…
We refer to the distance between optimal solutions of integer programs and their linear relaxations as proximity. In 2018, Eisenbrand and Weismantel proved that proximity is independent of the dimension for programs in standard form. We…
We continue the investigation of polynomial-time sparsification for NP-complete Boolean Constraint Satisfaction Problems (CSPs). The goal in sparsification is to reduce the number of constraints in a problem instance without changing the…
Decision procedures can be either theory-specific, e.g., Presburger arithmetic, or theory-generic, applying to an infinite number of user-definable theories. Variant satisfiability is a theory-generic procedure for quantifier-free…
Word equations are a crucial element in the theoretical foundation of constraint solving over strings, which have received a lot of attention in recent years. A word equation relates two words over string variables and constants. Its…
Word equations are a crucial element in the theoretical foundation of constraint solving over strings. A word equation relates two words over string variables and constants. Its solution amounts to a function mapping variables to constant…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…
While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…
This paper provides an NP procedure that decides whether a linear-exponential system of constraints has an integer solution. Linear-exponential systems extend standard integer linear programs with exponential terms $2^x$ and remainder terms…
Many important quantities of interest are only partially identified from observable data: the data can limit them to a set of plausible values, but not uniquely determine them. This paper develops a unified framework for covariate-assisted…