1 research outputs found
Formally Verified Compositional Algorithms for Factored Transition Systems
Artificial Intelligence (AI) planning and model checking are two
disciplines that found wide practical applications.
It is often the case that a problem in those two fields concerns
a transition system whose behaviour can be encoded in a digraph
that models the system's state space.
However, due to the very large size of state spaces of realistic
systems, they are compactly represented as propositionally
factored transition systems.
These representations have the advantage of being exponentially
smaller than the state space of the represented system.
Many problems in AI~planning and model checking involve questions
about state spaces, which correspond to graph theoretic questions
on digraphs modelling the state spaces.
However, existing techniques to answer those graph theoretic
questions effectively require, in the worst case, constructing
the digraph that models the state space, by expanding the
propositionally factored representation of the syste\
m.
This is not practical, if not impossible, in many cases because
of the state space size compared to the factored representation.
One common approach that is used to avoid constructing the state
space is the compositional approach, where only smaller
abstractions of the system at hand are processed and the given
problem (e.g. reachability) is solved for them.
Then, a solution for the problem on the concrete system is
derived from the solutions of the problem on the abstract
systems.
The motivation of this approach is that, in the worst case, one
need only construct the state spaces of the abstractions which
can be exponentially smaller than the state space of the concrete
system.
We study the application of the compositional approach to two
fundamental problems on transition systems: upper-bounding the
topological properties (e.g. the largest distance between any two
states, i.e. the diameter) of the state spa\
ce, and computing reachability between states.
We provide new compositional algorithms to solve both problems by
exploiting different structures of the given system.
In addition to the use of an existing abstraction (usually
referred to as projection) based on removing state space
variables, we develop two new abstractions for use within our
compositional algorithms.
One of the new abstractions is also based on state variables,
while the other is based on assignments to state variables.
We theoretically and experimentally show that our new
compositional algorithms improve the state-of-the-art in solving
both problems, upper-bounding state space topological parameters
and reachability.
We designed the algorithms as well as formally verified them with
the aid of an interactive theorem prover.
This is the first application that we are aware of, for such a
theorem prover based methodology to the design of new algorithms
in either AI~planning or model checking