The significance of state complexity in automata and regular languages? I'm reading "Concatenation of Regular Languages and Descriptional Complexity" by Galina Jiraskova, 2009 on the state complexity resulting from concatenation of two regular languages ( by Galina Jiraskova), but I can't understand what the practical implications of state complexity would be. The first trivial thought that struck me was that higher complexity would require more time and space by the machine. Is this correct? Also are there any other places where state complexity is relevant and signinficant? 

Edit:
The state complexity of a regular language is the smallest number of states in any
deterministic finite automaton (dfa) accepting the language. The nondeterministic
state complexity of a regular language is defined as the smallest number of states in any nondeterministic finite automaton (nfa) for the language.
State complexity is really about concise description of an object (in this case, a regular language), not about computational complexity.  The general topic is called "descriptional complexity" in the literature and draws its inspiration, in part, from the classic 1971 paper of Meyer and Fischer entitled "Economy of Expression by Automata, Grammars, and Formal Systems" (see http://people.csail.mit.edu/meyer/economy-of-description.pdf ).  This is still an active area, with a yearly conference (DCFS - Descriptional Complexity of Formal Systems).

As for applications, any place where your program essentially relies on a finite-state machine (e.g., parsers) it will be good to have this finite-state machine as small as possible.