IMFUFA Seminar: Program Inversion by Maja Kirkeby (RUC/IMT)

Program inversion is an elementary program to program transformation and is a generalization of the function inversion known from Mathematics.
Wednesday
15
September
Start:14:00
End:16:00
Place: Roskilde University 27.1, Room 1

Given a specification of the known input and output arguments of a program, a program inverter creates a new program where the known arguments are input, and the rest is output. There are three kinds of program inversions, namely full inversion, partial inversion and semi-inversion, where semi-inversion is the most general one. If p is a program with two inputs (x,y) and two outputs (u,v), then the three forms of inversion can be illustrated as follows.

p(x,y) = <u,v> == full inversion ==> p'(u,v) = <x,y>
p(x,y) = <u,v> == partial inversion ==> p'(x,u,v) = <y>
p(x,y) = <u,v> == semi inversion ==> p('x,v) = <u,y>

Full inversion swaps the entire input and output, partial inversion swaps parts of the input and the entire output, and semi-inversion allows parts of the input and output to be swapped. Important applications include the full inversion of lossless encoders, e.g., encode(data) = code into decode(code) = data, the partial inversion of symmetric encrypters, inverting, e.g., encrypt(key; data) = code into decrypt(key; code) = data, and the semiinversion of equation systems to isolate the unknown variables.

Program inversion algorithms are often tightly connected to a particular programming language, and instead, we use conditional constructor term rewriting systems; these systems model reversible, functional and declarative languages. In this talk, we present and discuss inverters developed for these rewrite systems.

Registration

The seminar is open for everyone, no registration needed.

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