Related papers: Classical Control, Quantum Circuits and Linear Log…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
We lay the foundations for a database-inspired approach to interpreting and understanding neural network models by querying them using declarative languages. Towards this end we study different query languages, based on first-order logic,…
We show that if a language is recognized within certain error bounds by constant-depth quantum circuits over a finite family of gates, then it is computable in (classical) polynomial time. In particular, our results imply EQNC^0 is…
Quantum circuit compilation comprises many computationally hard reasoning tasks that nonetheless lie inside #$\mathbf{P}$ and its decision counterpart in $\mathbf{PP}$. The classical simulation of general quantum circuits is a core example.…
In purely functional programming languages imperative features, more generally computational effects are prohibited. However, non-functional lan- guages do involve effects. The theory of decorated logic provides a rigorous for- malism (with…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
We argue that the quantum-theoretical structures studied in several recent lines of research cannot be adequately described within the standard framework of quantum circuits. This is in particular the case whenever the combination of…
$\{log\}$ is a programming language at the intersection of Constraint Logic Programming, set programming and declarative programming. But $\{log\}$ is also a satisfiability solver for a theory of finite sets and finite binary relations.…
We introduce the monoidal closed category qCPO of quantum cpos, whose objects are "quantized" analogs of omega-complete partial orders (cpos). The category qCPO is enriched over the category CPO of cpos, and contains both CPO, and the…
Separations among the first order logic ${\cal R}ing(0,+,*)$ of finite residue class rings, its extensions with generalized quantifiers, and in the presence of a built-in order are shown, using algebraic methods from class field theory.…
Differential linear categories provide the categorical semantics of the multiplicative and exponential fragments of Differential Linear Logic. Briefly, a differential linear category is a symmetric monoidal category that is enriched over…
We present an imperative quantum programming language LanQ which was designed to support combination of quantum and classical programming and basic process operations - process creation and interprocess communication. The language can thus…
Recent advances in quantum computing have opened new pathways for enhancing deep learning architectures, particularly in domains characterized by high-dimensional and context-rich data such as natural language processing (NLP). In this…
This paper defines a new proof- and category-theoretic framework for classical linear logic that separates reasoning into one linear regime and two persistent regimes corresponding to ! and ?. The resulting linear/producer/consumer (LPC)…
The ongoing digital transformation in industry applies to all product life cycle's stages. The design decisions and dimensioning carried out in the early conceptual design stages determine a huge part of the product's life cycle costs…
Existential rules, a.k.a. dependencies in databases, and Datalog+/- in knowledge representation and reasoning recently, are a family of important logical languages widely used in computer science and artificial intelligence. Towards a deep…
While much of the current study on quantum computation employs low-level formalisms such as quantum circuits, several high-level languages/calculi have been recently proposed aiming at structured quantum programming. The current work…
This work develops a formal framework for specifying, implementing, and analysing quantum communication protocols. We provide tools for developing simple proofs and analysing programs which involve communication, both via quantum channels…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…