相关论文: Combining decision procedures for the reals

By assuming a deterministic evolution of quantum systems and taking realism into account, we carefully build a hidden variable theory for Quantum Mechanics based on the notion of ontological states proposed by 't Hooft. We view these…

First-order linear real arithmetic enriched with uninterpreted predicate symbols yields an interesting modeling language. However, satisfiability of such formulas is undecidable, even if we restrict the uninterpreted predicate symbols to…

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…

We study the collection of first-order logical schemata all of whose instances are theorems of a given theory $T$; we call these the validities of $T$ ($\mathsf{V}(T)$). It is easy to see that if $T$ is a decidable theory, then…

This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable (in principle rather than in practice). Various problems in the context of…

Let a quantified inequality constraint over the reals be a formula in the first-order predicate language over the structure of the real numbers, where the allowed predicate symbols are $\leq$ and $<$. Solving such constraints is an…

We investigate the quantifier alternation hierarchy in first-order logic on finite words. Levels in this hierarchy are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…

An operational probabilistic theory where all systems are classical, and all pure states of composite systems are entangled, is constructed. The theory is endowed with a rule for composing an arbitrary number of systems, and with a…

We generalize the framework of virtual substitution for real quantifier elimination to arbitrary but bounded degrees. We make explicit the representation of test points in elimination sets using roots of parametric univariate polynomials…

Nominal Logic is a version of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to higher-order logic, bindable names, called atoms, and instantiable variables are considered as…

Models of a generalized nondeterminism are defined by limitations on nonde- terministic behavior of a computing device. A regular realizability problem is a problem of verifying existence of a special sort word in a regular language. These…

Given a single (differential-algebraic) input-output equation, we present a method for finding different representations of the associated system in the form of rational realizations; these are dynamical systems with rational right-hand…

We investigate quantifier alternation hierarchies in first-order logic on finite words. Levels in these hierarchies are defined by counting the number of quantifier alternations in formulas. We prove that one can decide membership of a…

We consider existential problems over the reals. Extended quantifier elimination generalizes the concept of regular quantifier elimination by providing in addition answers, which are descriptions of possible assignments for the quantified…

Monadic decomposibility --- the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas --- is a powerful tool for devising a decision procedure for a given logical…

Julia Robinson has given a first-order definition of the rational integers Z in the rational numbers Q by a formula (\forall \exists \forall \exists)(F=0) where the \forall-quantifiers run over a total of 8 variables, and where F is a…

The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment of first-order logic to contexts involving relations of arity greater than two. Quantifiers in this…

This article discusses completeness of Boolean Algebra as First Order Theory in Goedel's meaning. If Theory is complete then any possible transformation is equivalent to some transformation using axioms, predicates etc. defined for this…

The study of word equations (or the existential theory of equations over free monoids) is a central topic in mathematics and theoretical computer science. The problem of deciding whether a given word equation has a solution was shown to be…

Let $\RR_S$ denote the expansion of the real ordered field by a family of real-valued functions $S$, where each function in $S$ is defined on a compact box and is a member of some quasianalytic class which is closed under the operations of…