Abstract
This paper presents a method to generate characterizing definitions for finite and parameterized structures. In particular, the method is applied to generate a conjecture for the properties characterizing a special class of graphs, called superpositional graphs.
The method can be used if the exact set of properties that describes a given finite structure cannot be found by pure thought but we can find the number of objects for small values of the parameter.
The next step is to codify the objects as assignments to a set of propositional variables, and the candidate properties as propositional formulae, in such a way that an object satisfies the property if and only if the assignment satisfies the formula. The main idea of this method is to find models that do not fit with the current approximation of the description of the structure and stepwise refine the logical description.
Finally, we “translate” the logical description into a mathematical one and prove it.
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Peder, A., Tombak, M. (2011). Finding the Description of Structure by Counting Method: A Case Study. In: Černá, I., et al. SOFSEM 2011: Theory and Practice of Computer Science. SOFSEM 2011. Lecture Notes in Computer Science, vol 6543. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18381-2_38
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DOI: https://doi.org/10.1007/978-3-642-18381-2_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-18380-5
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