40 citations · 98 across the 22 of their papers we have counts for
13 papers · 1 filter
Composing Codensity Bisimulations
Mayuko Kori, Kazuki Watanabe, Jurriaan Rot +1
Proving compositionality of behavioral equivalence on state-based systems with respect to algebraic operations is a classical and widely studied problem. We study a categorical for…
The Lattice-Theoretic Essence of Property Directed Reachability Analysis
Mayuko Kori, Natsuki Urabe, Shin-ya Katsumata +2
We present LT-PDR, a lattice-theoretic generalization of Bradley's property directed reachability analysis (PDR) algorithm. LT-PDR identifies the essence of PDR to be an ingenious…
Higher-order probabilistic adversarial computations: Categorical semantics and program logics
Alejandro Aguirre, Gilles Barthe, Marco Gaboardi +3
Adversarial computations are a widely studied class of computations where resource-bounded probabilistic adversaries have access to oracles, i.e., probabilistic procedures with pri…
Expressivity of Quantitative Modal Logics: Categorical Foundations via Codensity and Approximation
Yuichi Komorida, Shin-ya Katsumata, Clemens Kupke +2
A modal logic that is strong enough to fully characterize the behavior of a system is called expressive. Recently, with the growing diversity of systems to be reasoned about (proba…
Fibrational Initial Algebra-Final Coalgebra Coincidence over Initial Algebras: Turning Verification Witnesses Upside Down
Mayuko Kori, Ichiro Hasuo, Shin-ya Katsumata
The coincidence between initial algebras (IAs) and final coalgebras (FCs) is a phenomenon that underpins various important results in theoretical computer science. In this paper, w…
Graded Hoare Logic and its Categorical Semantics
Marco Gaboardi, Shin-ya Katsumata, Dominic Orchard +1
Deductive verification techniques based on program logics (i.e., the family of Floyd-Hoare logics) are a powerful approach for program reasoning. Recently, there has been a trend o…
Interaction laws of monads and comonads
Shin-ya Katsumata, Exequiel Rivas, Tarmo Uustalu
We introduce and study functor-functor and monad-comonad interaction laws as mathematical objects to describe interaction of effectful computations with behaviors of effect-perform…
Codensity Games for Bisimilarity
Yuichi Komorida, Shin-ya Katsumata, Nick Hu +2
Bisimilarity as an equivalence notion of systems has been central to process theory. Due to the recent rise of interest in quantitative systems (probabilistic, weighted, hybrid, et…
Differentiable Causal Computations via Delayed Trace
David Sprunger, Shin-ya Katsumata
We investigate causal computations taking sequences of inputs to sequences of outputs where the th output depends on the first inputs only. We model these in category theory…
Relational Differential Dynamic Logic
Juraj Kolčák, Ichiro Hasuo, Jérémy Dubut +3
In the field of quality assurance of hybrid systems (that combine continuous physical dynamics and discrete digital control), Platzer's differential dynamic logic (dL) is widely re…
Codensity Lifting of Monads and its Dual
Shin-ya Katsumata, Tetsuya Sato, Tarmo Uustalu
We introduce a method to lift monads on the base category of a fibration to its total category. This method, which we call codensity lifting, is applicable to various fibrations wh…
Quantitative bisimulations using coreflections and open morphisms
Jérémy Dubut, Ichiro Hasuo, Shin-ya Katsumata +1
We investigate a canonical way of defining bisimilarity of systems when their semantics is given by a coreflection, typically in a category of transition systems. We use the fact,…
Extensional Models of Untyped Lambda-mu Calculus
Koji Nakazawa, Shin-ya Katsumata
This paper proposes new mathematical models of the untyped Lambda-mu calculus. One is called the stream model, which is an extension of the lambda model, in which each term is inte…