DeepAI AI Chat
Log In Sign Up

Generalising KAT to verify weighted computations

by   Leandro Gomes, et al.

Kleene algebra with tests (KAT) was introduced as an algebraic structure to model and reason about classic imperative programs, i.e. sequences of discrete transitions guarded by Boolean tests. This paper introduces two generalisations of this structure able to express programs as weighted transitions and tests with outcomes in non necessarily bivalent truth spaces: graded Kleene algebra with tests (GKAT) and a variant where tests are also idempotent (I-GKAT). On this context, and in analogy to Kozen's encoding of Propositional Hoare Logic (PHL) in KAT [22], we discuss the encoding of a graded PHL in I-GKAT and of its while-free fragment in GKAT. Moreover, to establish semantics for these structures four new algebras are defined: FSET(T), FREL(K,T) and FLANG(K,T) over complete residuated lattices K and T, and M(n,A) over a GKAT or I-GKAT A. As a final exercise, the paper discusses some program equivalence proofs in a graded context.


page 1

page 2

page 3

page 4


Kleene Algebra With Tests for Weighted Programs

Weighted programs generalize probabilistic programs and offer a framewor...

A Complete Inference System for Skip-free Guarded Kleene Algebra with Tests

Guarded Kleene Algebra with Tests (GKAT) is a fragment of Kleene Algebra...

Algebraic Reasoning of Quantum Programs via Non-Idempotent Kleene Algebra

We investigate the algebraic reasoning of quantum programs inspired by t...

One-sorted Program Algebras

Kleene algebra with tests, KAT, provides a simple two-sorted algebraic f...

Kleene Algebra with Observations

Kleene algebra with tests (KAT) is an algebraic framework for reasoning ...

From Equations to Distinctions: Two Interpretations of Effectful Computations

There are several ways to define program equivalence for functional prog...

Processes Parametrised by an Algebraic Theory

We develop a (co)algebraic framework to study a family of process calcul...