Related papers: Higher-Order Pattern Complement and the Strict Lam…

Alternating automata have been widely used to model and verify systems that handle data from finite domains, such as communication protocols or hardware. The main advantage of the alternating model of computation is that complementation is…

We outline refined versions of two major quantum algorithms for performing principal component analysis and solving linear equations. Our methods are exponentially faster than their classical counterparts and even previous quantum…

We propose a model-based approach to the model checking problem for recursive schemes. Since simply typed lambda calculus with the fixpoint operator, lambda-Y-calculus, is equivalent to schemes, we propose the use of a model of…

This Survey provides an overview of techniques in termination analysis for programs with numerical variables and transitions defined by linear constraints. This subarea of program analysis is challenging due to the existence of undecidable…

Answering logical queries over incomplete knowledge bases is challenging because: 1) it calls for implicit link prediction, and 2) brute force answering of existential first-order logic queries is exponential in the number of existential…

We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…

Two distinct research approaches have been proposed for assigning a purely extensional semantics to higher-order logic programming. The former approach uses classical domain theoretic tools while the latter builds on a fixed-point…

Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…

We present a new lambda-calculus with explicit substitutions and named variables. Renaming of bound variables in this calculus is explicit (there is a special rewrite rule) and can be delayed. Contexts (environments) are not sets or lists…

Higher-order representations of objects such as programs, proofs, formulas and types have become important to many symbolic computation tasks. Systems that support such representations usually depend on the implementation of an intensional…

To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…

Higher-order beta-matching is the following decision problem: given two simply typed lambda-terms, can the first term be instantiated to be beta-equivalent to the second term? This problem was formulated by Huet in the 1970s and shown…

We present a sequent calculus for first-order logic with lambda terms and definite descriptions. The theory formalised by this calculus is essentially Russellian, but avoids some of its well known drawbacks and treats definite description…

We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…

We investigate an extension of nominal many-sorted signatures in which abstraction has a form of instantiation, called generalised concretion, as elimination operator (similarly to lambda-calculi). Expressions are then classified using a…

We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this…

This paper presents the Functional Machine Calculus (FMC) as a simple model of higher-order computation with "reader/writer" effects: higher-order mutable store, input/output, and probabilistic and non-deterministic computation. The FMC…

The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while…

First-order model counting (FOMC) is a computational problem that asks to count the models of a sentence in finite-domain first-order logic. In this paper, we argue that the capabilities of FOMC algorithms to date are limited by their…

We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…