50 research outputs found
Polynomial Invariants for Affine Programs
We exhibit an algorithm to compute the strongest polynomial (or algebraic)
invariants that hold at each location of a given affine program (i.e., a
program having only non-deterministic (as opposed to conditional) branching and
all of whose assignments are given by affine expressions). Our main tool is an
algebraic result of independent interest: given a finite set of rational square
matrices of the same dimension, we show how to compute the Zariski closure of
the semigroup that they generate
Pattern graph rewrite systems
String diagrams are a powerful tool for reasoning about physical processes,
logic circuits, tensor networks, and many other compositional structures.
Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric
representations of string diagrams, amenable to automated reasoning about
diagrammatic theories via graph rewrite systems. In this extended abstract, we
show how the power of such rewrite systems can be greatly extended by
introducing pattern graphs, which provide a means of expressing infinite
families of rewrite rules where certain marked subgraphs, called !-boxes ("bang
boxes"), on both sides of a rule can be copied any number of times or removed.
After reviewing the string graph formalism, we show how string graphs can be
extended to pattern graphs and how pattern graphs and pattern rewrite rules can
be instantiated to concrete string graphs and rewrite rules. We then provide
examples demonstrating the expressive power of pattern graphs and how they can
be applied to study interacting algebraic structures that are central to
categorical quantum mechanics.Comment: In Proceedings DCM 2012, arXiv:1403.757
Musings on Encodings and Expressiveness
This paper proposes a definition of what it means for one system description
language to encode another one, thereby enabling an ordering of system
description languages with respect to expressive power. I compare the proposed
definition with other definitions of encoding and expressiveness found in the
literature, and illustrate it on a case study: comparing the expressive power
of CCS and CSP.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244
The Containment Problem for Unambiguous Register Automata
We investigate the complexity of the containment problem "Does L(A)subseteq L(B) hold?", where B is an unambiguous register automaton and A is an arbitrary register automaton. We prove that the problem is decidable and give upper bounds on the computational complexity in the general case, and when B is restricted to have a fixed number of registers