A Coalgebraic Approach to Kleene Algebra with Tests
Hubie Chen, Riccardo Pucella
Abstract
Kleene algebra with tests is an extension of Kleene algebra, the algebra of regular expressions, which can be used to reason about programs. We develop a coalgebraic theory of Kleene algebra with tests, along the lines of the coalgebraic theory of regular expressions based on deterministic automata. Since the known automata-theoretic presentation of Kleene algebra with tests does not lend itself to a coalgebraic theory, we define a new interpretation of Kleene algebra with tests expressions and a corresponding automata-theoretic presentation. One outcome of the theory is a coinductive proof principle, that can be used to establish equivalence of our Kleene algebra with tests expressions.
Create a lesson
Related papers
Towards Finite Satisfiability of PDL with Loops
Bartosz Jan Bednarczyk, Mikołaj Swoboda
Vision-Predictor-Action: Towards Efficient Embodied AI via Neuro-Symbolic JEPA Predictors
Yeonseok Lee
Representation Theorems for Actual Powers over Two-Agent General Concurrent Game Frames
Zixuan Chen, Fengkui Ju, Thomas Ågotnes
Capturing Bisimulation-Invariant Exponential-Space Complexity Classes
Florian Bruse, David Kronenberger, Martin Lange
StructHCP: Structure-Aware SAT--CEGAR for the Hamiltonian Cycle Problem
Quan Van Vi, Tuyen Van Kieu, Khanh Van To
Solving Distributed Flexible Job Shop Scheduling Problem Using SAT
Phuong Dang Anh, Duc Nguyen Kim Trung, To Van Khanh