Abstract
The main goal of this chapter is to explain in a comprehensible way the semantic context in formal language theory. This is necessary to properly understand the attempts to extend Grammatical Evolution (GE) to include semantics. Several approaches from different researchers to handle semantics, both directly and indirectly, will be briefly introduced. Finally, previous works by the authors will be described in depth.
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Notes
- 1.
Let’s consider f as f: [0, |w|] → [−|w|, |w|] so that f(i) = ♯ a(w[0, i]) − ♯ b(|w[0, i]) and where w[0, i] is the subsequence of w respectively starting and ending in 0 and i. It is clear that |f(i + 1) − f(i)| = 1∀i. For this step of the proof, it is easy to consider either a version of Bonzano’s theorem for this kind of functions; or to define a function to which Bolzano’s result could be applied. In the first case, notice that for every zero of f (∀i|f(i) = 0); the sequence of points {(i, −1), (i, 0), (i, 1)} (or {(i, 1), (i, 0), (i, −1)}) always belongs to f. In the last case, one could consider the continuous function f′ that can be drawn connecting consecutive points of f or even a polynomial interpolation that preserves its points (all of them or at least the most relevant, around its zeros).
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Acknowledgements
This work has been supported by several research grants: Spanish Ministry of Science and Education under Project Code TIN2014-56494-C4-4-P (ephemeCH) and TIN2017-85727-C4-3-P (DeepBio). We thank also Manuel Alfonseca’s help to improve this work.
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de la Cruz Echeandía, M., Elhaddad, Y.R.S., Awinat, S., Ortega, A. (2018). GE and Semantics. In: Ryan, C., O'Neill, M., Collins, J. (eds) Handbook of Grammatical Evolution. Springer, Cham. https://doi.org/10.1007/978-3-319-78717-6_8
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