7 research outputs found
Contractions, Removals and How to Certify 3-Connectivity in Linear Time
It is well-known as an existence result that every 3-connected graph G=(V,E)
on more than 4 vertices admits a sequence of contractions and a sequence of
removal operations to K_4 such that every intermediate graph is 3-connected. We
show that both sequences can be computed in optimal time, improving the
previously best known running times of O(|V|^2) to O(|V|+|E|). This settles
also the open question of finding a linear time 3-connectivity test that is
certifying and extends to a certifying 3-edge-connectivity test in the same
time. The certificates used are easy to verify in time O(|E|).Comment: preliminary versio
Formally Verified SAT-Based AI Planning
We present an executable formally verified SAT encoding of classical AI
planning. We use the theorem prover Isabelle/HOL to perform the verification.
We experimentally test the verified encoding and show that it can be used for
reasonably sized standard planning benchmarks. We also use it as a reference to
test a state-of-the-art SAT-based planner, showing that it sometimes falsely
claims that problems have no solutions of certain lengths
From Algorithms to Working Programs On the Use of Program Checking in LEDA
We report on the use of program checking in the LEDA library of efficient data types and algorithms