We can represent the canonical automaton of a language as the smallest automaton which contains any other automaton recognizing this language, providing equivalent states are merged. Indeed, the canonical automaton appears to be a good representative element in the equivalence class of non-deterministic automata recognizing a given language. Our aim is to provide a detailed description of the canonical automaton based on the notions of syntactical rectangle and characteristic event. In our approach, a state of the canonical automaton of a language L is associated with a rectangle (L,R) Í S*×S*, which is maximal w.r.t. the property L.R Í L. We explicit the link with other characterizations, like considering a state as a residual intersection which was given by Arnold et al., and the fundamental automaton defined by Matz and Potthoff. In particular, we pretend that the construction of the canonical automaton has the same time complexity as the construction of the fundamental automaton. Our last section briefly discusses the problem of searching minimal NFAs using the canonical automaton.
Light oil (isooctane) removal using soil vapor extraction (SVE) enhanced bioremediation (BR) was investigated by four steps, including: (i)amendment of substrates in batches (ii)continuous induction of contaminants for 15 days (iii)in situ acclimation for 100 days (iv)biodegradation assisted with SVE venting for 120 h at 20 m³∙h⁻¹ Results showed that the total removal efficiency was up to 90% after BR-SVE treatments. BR contributed predominantly to isooctane removal during the last 36 h of BR-SVE treatment. This implied that it would be an important strategy to limit water content at the early stage while increasing water supply at the end stage during implementation of BR-SVE, because water content was a significant factor hindering SVE but favoring BR. The overall results demonstrated a good complementarity between SVE and BR, and a potential for their combination in real-world applications.
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