Related papers: Reducing the Complexity of Quantified Formulas via…
In this contribution we derive and analyze a new numerical method for kinetic equations based on a variable transformation of the moment approximation. Classical minimum-entropy moment closures are a class of reduced models for kinetic…
We consider the Quantifier Elimination (QE) problem for propositional CNF formulas with existential quantifiers. QE plays a key role in formal verification. Earlier, we presented an approach based on the following observation. To perform…
In this paper we present an alternative approach to formalize the theory of logic programming. In this formalization we allow existential quantified variables and equations in queries. In opposite to standard approaches the role of answer…
Earlier, we introduced Partial Quantifier Elimination (PQE). It is a $\mathit{generalization}$ of regular quantifier elimination where one can take a $\mathit{part}$ of the formula out of the scope of quantifiers. We apply PQE to CNF…
In this paper, we present a general realizability semantics for the simply typed $\lambda\mu$-calculus. Then, based on this semantics, we derive both weak and strong normalization results for two versions of the $\lambda\mu$-calculus…
The unification algorithm has long been a target for program synthesis research, but a fully automatic derivation remains a research goal. In deductive program synthesis, computer programming is phrased as a task in theorem proving; a…
Given a formula $F$ of satisfiability modulo theory (SMT), the classical SMT solver tries to (1) abstract $F$ as a Boolean formula $F_B$, (2) find a Boolean solution to $F_B$, and (3) check whether the Boolean solution is consistent with…
Recent developemnts in string compactifications in the presence of antisymmetric field backgrounds suggest a new simple and predictive structure for soft terms in the MSSM depending only on two parameters. They give rise to a positive…
The decomposition of arbitrary unitary transformations into sequences of simpler, physically realizable operations is a foundational problem in quantum information science, quantum control, and linear optics. We establish a 1D Quantum Field…
Generalization problems in languages with binders involve computing the most common structure between expressions while respecting bound variable renaming and freshness constraints. These problems often lack a least general solution.…
While symmetries are well understood for Boolean formulas and successfully exploited in practical SAT solving, less is known about symmetries in quantified Boolean formulas (QBF). There are some works introducing adaptions of propositional…
Boolean satisfiability (SAT) is a fundamental NP-complete problem with many applications, including automated planning and scheduling. To solve large instances, SAT solvers have to rely on heuristics, e.g., choosing a branching variable in…
This paper presents a simplified method of expressing the solution to cubic equations in terms of function evaluation only. The method eliminates the need to manipulate the original coefficients of the cubic polynomial and makes the…
We analyze possibilities of second-order quantifier elimination for formulae containing parameters -- constants or functions. For this, we use a constraint resolution calculus obtained from specializing the hierarchical superposition…
In this paper, a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways: (i) a number of different types of quantifiers (logical, absolute, proportional,…
Change-of-variables (CoV) formulas allow to reduce complicated probability densities to simpler ones by a learned transformation with tractable Jacobian determinant. They are thus powerful tools for maximum-likelihood learning, Bayesian…
Term algebras are important objects in computer science and are correspondingly well-studied. A natural generalization is to quotient these algebras by finitely many ground term equations, obtaining what we call almost free algebras. One of…
A new characterization of provably recursive functions of first-order arithmetic is described. Its main feature is using only terms consisting of 0, the successor S and variables in the quantifier rules, namely, universal elimination and…
In this work, we discuss two modifications that can be made to a known variational quantum singular value decomposition algorithm popular in the literature. The first is a change to the objective function which hints at improved performance…
We describe the design of a quantifier elimination framework for the complex numbers in the language of ordered rings supplemented with symbols for the imaginary unit, real parts, imaginary parts, and conjugates. Technically, we use a…