Time Warps, from Algebra to Algorithms

Guatto, Adrien; Metcalfe, George; Santschi, Simon

doi:10.1007/978-3-030-88701-8_19

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2023

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“…That is, an algorithm is required that decides equations between terms interpreted over the algebraic structure of time warps. In a precursor to this paper [25], decidability of the equational theory of the bounded residuated lattice W, ∧, ∨, •, \, /, id, ⊥, ⊤ , with least and greatest time warps ⊥ and ⊤, respectively, was established. A key ingredient of the proof, however, involves translating terms into a rather awkward normal form which both complicates the decision procedure and obscures the algebraic meaning of the equations.…”

Section: Introductionmentioning

confidence: 99%

Deciding Equations in the Time Warp Algebra

Guatto¹,

Metcalfe²,

Santschi³

2023

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Join-preserving maps on the discrete time scale ω + , referred to as time warps, have been proposed as graded modalities that can be used to quantify the growth of information in the course of program execution. The set of time warps forms a simple distributive involutive residuated lattice-called the time warp algebra-that is equipped with residual operations relevant to potential applications. In this paper, we show that although the time warp algebra generates a variety that lacks the finite model property, it nevertheless has a decidable equational theory. We also describe an implementation of a procedure for deciding equations in this algebra, written in the OCaml programming language, that makes use of the Z3 theorem prover.

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Section: Introductionmentioning

confidence: 99%