Symbolic pattern manipulation of Karnaugh-Veitch maps for pneumatic circuits

Pneumatics continue to play a vital role in low-cost automation. The designing of pneumatic control circuits has to date been a slow manual process. This paper describes the computational symbolic manipulation of the Karnaugh-Veitch (KV) map which is the heart of the prototype expert system called PNEUMAES. The symbolic manipulation of a KV map is governed by two sets of generic rules for signal flow plotting and for logic equation minimisation applicable for complex pneumatic circuits. As the complexity of the circuit increases, the symbolic manipulation of a KV map leads to the combinatorial explosion problem. Because of this problem, PNEUMAES can only automatically generate pure pneumatic circuit design equations which will yield minimised circuit configuration for up to four cylinders with auxiliary control valves. A case study is included and issues and problems relating to the implementation of the KV map are discussed. Symbolic and sub-symbolic learning approaches are suggested as a means by which the search space of the symbolic patterns of the KV map can be pruned.