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By Torben Ægidius Mogensen

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Hence, all the DFA states are distinct, so the DFA is minimal. 10. 2 45 Limits to expressive power The most basic property of a DFA is that it is finite: It has a finite number of states and nowhere else to store information. This means, for example, that any language that requires unbounded counting cannot be regular. An example of this is the language {❛n ❜n | n ≥ 0}, that is, any sequence of ❛s followed by a sequence of the same number of ❜s. If we must decide membership in this language by a DFA that reads the input from left to right, we must, at the time we have read all the ❛s, know how many there were, so we can compare this to the number of ❜s.

12, all regular expressions share the same starting state. , for both tokens in the programming language and for tokens in the input to that language. Often, there will be a good deal of sharing between these token sets (the tokens allowed in the input may, for example, be a subset of the tokens allowed in programs). Hence, it is useful to allow these to share a NFA, as this will save space. The resulting DFA will have several starting states. An accepting state may now have more than one token name attached, as long as these come from different token sets (corresponding to different starting points).

As all finite sets of strings are regular languages, the set of all legal Pascal programs of less than a million pages is a regular language, though it is by no means a simple one. While it can be argued that it would be an acceptable limitation for a language to allow only programs of less than a million pages, it is not practical to describe a programming language as a regular language: The description would be far too large. Even if we ignore such absurdities, we can sometimes be surprised by the expressive power of regular languages.

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