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Questions tagged [automata]

Questions about mathematical devices that read an input stream symbol by symbol and use a state transition map to produce an output stream, maybe using secondary storage.

Automata, or state machines, are mathematical devices often used to define formal languages by way of accepting, or recognizing, or deciding strings belonging to the target language. Commonly encountered varieties of automata are finite automata, pushdown automata, linear-bounded automata, and Turing machines.

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Is a Turing Machine "by definition" the most powerful machine?

I agree that a Turing Machine can do "all possible mathematical problems". But that is because it is just a machine representation of an algorithm: first do this, then do that, finally output that. I mean anything that is solvable can be…
Sounak Bhattacharya
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How to prove a language is regular?

There are many methods to prove that a language is not regular, but what do I need to do to prove that some language is regular? For instance, if I am given that $L$ is regular, how can I prove that the following $L'$ is regular, too? $\qquad…
corium
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Is a push-down automaton with two stacks equivalent to a turing machine?

In this answer it is mentioned A regular language can be recognized by a finite automaton. A context-free language requires a stack, and a context sensitive language requires two stacks (which is equivalent to saying it requires a full Turing…
Lazer
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Determining capabilities of a min-heap (or other exotic) state machines

See the end of this post for some clarification on the definition(s) of min-heap automata. One can imagine using a variety of data structures for storing information for use by state machines. For instance, push-down automata store information in a…
Patrick87
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Are there inherently ambiguous and deterministic context-free languages?

Let us call a context-free language deterministic if and only if it can be accepted by a deterministic push-down automaton, and nondeterministic otherwise. Let us call a context-free language inherently ambiguous if and only if all context-free…
Patrick87
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Are there any non-finite automata?

In automata theory, we all read automata as finite automata, from the very beginning. What I want to know is, why are automata finite? To be clear, what is it in an automaton that is finite - the alphabet, language, strings made with regular…
parvin
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What is the significance of context-sensitive (Type 1) languages?

Seeing that in the Chomsky Hierarchy Type 3 languages can be recognised by a state machine with no external memory (i.e., a finite automaton), Type 2 by a state machine with a single stack (i.e. a push-down automaton) and Type 0 by a state machine…
bitmask
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How to simulate backreferences, lookaheads, and lookbehinds in finite state automata?

I created a simple regular expression lexer and parser to take a regular expression and generate its parse tree. Creating a non-deterministic finite state automaton from this parse tree is relatively simple for basic regular expressions. However I…
Aadit M Shah
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How to show that a "reversed" regular language is regular

I'm stuck on the following question: "Regular languages are precisely those accepted by finite automata. Given this fact, show that if the language $L$ is accepted by some finite automaton, then $L^{R}$ is also accepted by some finite; $L^{R}$…
Cat
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Equivalence of Büchi automata and linear $\mu$-calculus

It's a known fact that every LTL formula can be expressed by a Büchi $\omega$-automaton. But, apparently, Büchi automata are a more powerful, expressive model. I've heard somewhere that Büchi automata are equivalent to linear-time $\mu$-calculus…
Daniil
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Why is non-determinism a useful concept?

An automaton is an abstract model of a digital computer. Digital computers are completely deterministic; their state at any time is uniquely predictable from the input and the initial state. When we are trying to model real systems, why include…
Tanmoy Banerjee
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How is the rule 110 Turing complete?

I've read the wikipedia page for rule 110 in cellular automata, and I more or less know how they work (a set of rules decides where to draw the next 1 or 0). I've just read they're Turing complete, but I can't even fathom how would you 'program' in…
AncientSwordRage
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What are the conditions for a NFA for its equivalent DFA to be maximal in size?

We know that DFAs are equivalent to NFAs in expressiveness power; there is also a known algorithm for converting NFAs to DFAs (unfortunately I do now know the inventor of that algorithm), which in worst case gives us $2^S$ states, if our NFA had $S$…
Daniil
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Decide whether a context-free languages can be accepted by a deterministic pushdown automaton

Given a context-free grammar G, there exists a Nondeterministic Pushdown Automaton N that accepts exactly the language G accepts. (and visa versa) There may also exist a Deterministic Pushdown Automaton D that accepts exactly the language G accepts…
Andrew Tomazos
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How to prove that DFAs from NFAs can have exponential number of states?

All non-deterministic finite automata can be turned into equivalent deterministic finite automata. However, a deterministic finite automata only allows a single arrow per symbol pointing from a state. Therefore, its states should be members of the…
John Hoffman
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