This paper develops verification methodology for quantum programs, and the
contribution of the paper is two-fold: 1. Sharir, Pnueli and Hart [SIAM J.
Comput. 13(1984)292-314] presented a general method for proving properties of
probabilistic programs, in which a probabilistic program is modeled by a Markov
chain and an assertion on the output distribution is extended into an invariant
assertion on all intermediate distributions.
Direction relations between extended spatial objects are important
commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model,
known as Cardinal Direction Calculus (CDC), for representing direction
relations between connected plane regions. CDC is perhaps the most expressive
qualitative calculus for directional information, and has attracted increasing
interest from areas such as artificial intelligence, geographical information
science, and image retrieval.