You are probably thinking of Temporal logic which allows us to model if algorithms and programs terminate etc! It can be represented by using state machines tho!

For the purpose of algorithm verification, the final and/or pushdown automaton or probably sometimes even Turing Machines are used, because they are easier to work with. "Real" regular expressions are only nice to write a grammar for regular languages which can be easily interpreted by the computer I think. The thing is, that regexs in the *nix and programming language world are also used for searching which is why there are additional special characters to indicate things like: "it has to end with ..." and there are shortcuts for when you want that a character or sequence occurs

• at least once,
• once or never or
• a specified number of times back to back.

In "standard" regex, you would only have

• () for grouping,
• * for 0 or any number of occurances (so a* means blank or a or aa or ...)
• + as combining two characters/groups with exclusive or (in programming, a+ is mostly the same as aa* so this is a difference)
• and sometimes some way to have a shortcut for (a+b+c+...+z) if you want to allow any lower case character as the next one

So there are only 4 characters which have the same expressive power as the extended syntax with the exception of not being able to indicate, that it should occur at the end or beginning of a string/line (which could even be removed if one would have implemented different functions or options for the tools we now have instead)

So one could say that *nix regex is bloated /s