Related papers: Weak Similarity in Higher-Order Mathematical Opera…
Submodularity is an important concept in integer and combinatorial optimization. A classical submodular set function models the utility of selecting homogenous items from a single ground set, and such selections can be represented by binary…
There is increasing interest in learning algorithms that involve interaction between human and machine. Comparison-based queries are among the most natural ways to get feedback from humans. A challenge in designing comparison-based…
We argue that the implementation and verification of compilers for functional programming languages are greatly simplified by employing a higher-order representation of syntax known as Higher-Order Abstract Syntax or HOAS. The underlying…
We give a leisurely introduction to our abstract framework for operational semantics based on cellular monads on transition categories. Furthermore, we relate it for the first time to an existing format, by showing that all Positive GSOS…
The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…
Weakest preconditions are a useful notion for program verification as they reduce a problem of program verification to a problem of constraint solving. Category-theoretic generalisations of weakest preconditions have been studied to capture…
We have recently defined a weak Markovian bisimulation equivalence in an integrated-time setting, which reduces sequences of exponentially timed internal actions to individual exponentially timed internal actions having the same average…
Levy's call-by-push-value is a comprehensive programming paradigm that combines elements from functional and imperative programming, supports computational effects and subsumes both call-by-value and call-by-name evaluation strategies. In…
The study of well quasi-orders, wqo, is a cornerstone of combinatorics and within wqo theory Kruskal's theorem plays a crucial role. Extending previous proof-theoretic results, we calculate the $\Pi^1_1$ ordinals of two different versions…
We consider lambda-Y-calculus as a non-interpreted functional programming language: the result of the execution of a program is its normal form that can be seen as the tree of calls to built-in operations. Weak monadic second-order logic…
In this thesis, a comprehensive formalization of Milner's Calculus of Communicating Systems (also known as CCS) has been done in HOL theorem prover (HOL4), based on an old work in HOL88. This includes all classical properties of strong/weak…
In this paper, we provide tight lower bounds for the oracle complexity of minimizing high-order H\"older smooth and uniformly convex functions. Specifically, for a function whose $p^{th}$-order derivatives are H\"older continuous with…
Recently, some general frameworks have been proposed as unifying theories for processes combining non-determinism with quantitative aspects (such as probabilistic or stochastically timed executions), aiming to provide general results and…
Bisimulation up-to enhances the coinductive proof method for bisimilarity, providing efficient proof techniques for checking properties of different kinds of systems. We prove the soundness of such techniques in a fibrational setting,…
Strong variational sufficiency is a newly proposed property, which turns out to be of great use in the convergence analysis of multiplier methods. However, what this property implies for non-polyhedral problems remains a puzzle. In this…
Higher-order tensor methods were recently proposed for minimizing smooth convex and nonconvex functions. Higher-order algorithms accelerate the convergence of the classical first-order methods thanks to the higher-order derivatives used in…
The concurrent refinement algebra has been developed to support rely/guarantee reasoning about concurrent programs. The algebra supports atomic commands and defines parallel composition as a synchronous operation, as in Milner's SCCS. In…
General frameworks have been recently proposed as unifying theories for processes combining non-determinism with quantitative aspects (such as probabilistic or stochastically timed executions), aiming to provide general results and tools.…
Operator learning offers a powerful paradigm for solving parametric partial differential equations (PDEs), but scaling probabilistic neural operators such as the recently proposed Gaussian Processes Operators (GPOs) to high-dimensional,…
In this paper, we show that theory of processes can be reduced to the theory of spatial logic. Firstly, we propose a spatial logic SL for higher order pi-calculus, and give an inference system of SL. The soundness and incompleteness of SL…