Automatic generation of linear-time algorithms from predicate calculus descriptions of problems on recursively constructed graph families.

*(English)*Zbl 0753.05062Summary: This paper describes a predicate calculus in which graph problems can be expressed. Any problem possessing such an expression can be solved in linear time on any recursively constructed graph, once its decomposition tree is known. Moreover, the linear-time algorithm can be generated automatically from the expression, because all our theorems are proved constructively. The calculus is founded upon a short list of particularly primitive predicates, which in turn are combined by fundamental logical operations. This framework is rich enough to include the vast majority of known linear-time solvable problems.

We have obtained these results independently of similar results by B. Courcelle, through utilization of the framework of W. M. Bern, E. L. Lawler and A. L. Wong [J. Algorithms 8, 216-235 (1987; Zbl 0618.68058)]. We believe our formalism is more practical for programmers who would implement the automatic generation machinery, and more readily understood by many theorists.

We have obtained these results independently of similar results by B. Courcelle, through utilization of the framework of W. M. Bern, E. L. Lawler and A. L. Wong [J. Algorithms 8, 216-235 (1987; Zbl 0618.68058)]. We believe our formalism is more practical for programmers who would implement the automatic generation machinery, and more readily understood by many theorists.

##### MSC:

05C85 | Graph algorithms (graph-theoretic aspects) |

68Q25 | Analysis of algorithms and problem complexity |

03B10 | Classical first-order logic |

68R10 | Graph theory (including graph drawing) in computer science |

##### Keywords:

linear-time algorithms; recursive graph class; automatic algorithm generation; predicate calculus; decomposition tree
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\textit{R. B. Borie} et al., Algorithmica 7, No. 5--6, 555--581 (1992; Zbl 0753.05062)

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