Automata theory: understanding different automata

[Avichal]

Move this thread to appropriate sub-forum if not here.

I'm studying automata theory and I'm having trouble understanding different machines or automata.
First one is regular language. This is the simplest machine with different states and we can switch depending on what our input is. Very well till here.

Then comes context-free languages. Now I fail to understand the need to study this machine. Along with different states it has a stack to. So in someway it can count also.
I get a little bit of intuition but not completely.

I don't understand need to study context-free language and turing-complete language? I need the intuition

 

[Greg Bernhardt]

I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?

 

[FactChecker]

My two cents: A stack can provide order of events / operations that is far easier than defining states for every possible sequence. Ten items can be put into 3.6 million different orders (permutations) in a stack. Imagine trying to define a state for each possible order.

 

[AlephZero]

Regular languages are easy to implement but they are too restrictive for many applications.

You can't describe many "simple" features of the a language using only a regular grammar. For example you can't write a regular grammar that will recognize the (infinite number of) strings

ab, aabb, aaabbb, aaaabbbb ... etc, where the string contains an arbitrary number of a's followed by the same number of b's.

That isn't just a "made up" example. It is the first step towards recognizing if pairs of characters like { } [ ] ( ) are correctly nested (to any depth) in the syntax of a programming language like C, Java, etc.

You could easily write a computer program to recognize strings like the above example, by using a variable to count the number of a's, and then count the same number of b's. In a context-free language, a stack can do that sort of counting operation, by push things onto the stack and popping the same number of things off it.

Context-free languages and Turing complete languages are needed to deal with "real world" situations that are too complex for regular expressions.

 

[LudusRex]

Automata theory is a branch of computer science and mathematics that deals with the study of abstract machines, or automata, and their computational abilities. These automata are used to model and understand the behavior of various computational devices, such as computers and robots.

The first concept in automata theory is that of regular languages. These are the simplest machines, with a finite number of states and the ability to switch between states based on input. They are useful for modeling and recognizing patterns in strings of characters, such as in text processing.

Context-free languages, on the other hand, are more complex machines that have the ability to count and manipulate a stack. They are used to model and analyze programming languages and their grammatical structures. Understanding context-free languages is important for designing efficient compilers and parsers, which are essential tools in software development.

Turing-complete languages are the most powerful machines in automata theory. They are capable of performing any computation that can be done by a computer, making them essential for understanding the limits of computation and for designing new programming languages and algorithms.

In summary, the study of different automata, including regular, context-free, and Turing-complete machines, is crucial for understanding the capabilities and limitations of computational devices. Each type of automaton has its own unique properties and applications, and a thorough understanding of them is essential for advancements in computer science and technology.