Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [finite-state-machine]

For questions about finite state machine, which is a mathematical model of computation.

A finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of states at any given time. The FSM can change from one state to another in response to some external inputs; the change from one state to another is called a transition. An FSM is defined by a list of its states, its initial state, and the conditions for each transition. Finite state machines are of two types – deterministic finite state machines and non-deterministic finite state machines. A deterministic finite-state machine can be constructed equivalent to any non-deterministic one.

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What is the period of Langton's ant on a torus?

Langton's ant runs on an infinite white grid. At every white square, it turns right, flips the color of the square, and moves forward one square. At every black square, it turns left, flips the color of the square, and moves forward one square.…
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Is it possible for a finite state machine to detect if a string has the same number of ones as zeros?

I'm having difficulty with a seemingly simple question. "Is it possible to have a finite state machine that detects if a bit string of arbitrary length has the same number of zeros as ones? If so what would it look like"? In trying to solve this…
Tommy
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Random search for very big Collatz conjecture counter-examples

I know that exhaustive search was done to test numbers up to 2^68. This seems like a big number but when looking at Collatz function as a Turing machine manipulating some input bit sequence, only sequences up to 68 bits were tested. Maybe something…
PanJanek
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FSM and regular language

Here is a finite state machine which can be recognised with a regular language. The regular expression which I've got for this FSM is: (10(0+(10))*11+11+00*10(0+(10))*11+00*11)(0+1)* Is this correct? If so how do I keep simplifying the expression…
Marx
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Can we construct groups of several discrete "loops"?

I know that we have cyclic groups. Maybe the groups which in the most easy-to-access way can explain the concept of a generator. But do there also exist groups of two or more loops? For example $\cases{{g_1}^{n_1} = e\\{g_2}^{n_2} = e}$ With…
mathreadler
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Advanced Math for Reinfrocement Learning - state space and state sequences (policies)

Reinforcement learning has two important notions and I am interested in advanced math that can investigate those notions: State space - set of states. Apparently, deep structures should exist in this space. E.g. (in the robotics applications) some…
TomR
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How math deals with state or "algebra of sequential logic"

Boolean algebra is well-studied and you could easily find a lot of introductory materials on different operators, properties, how eveything is nicely related to the algebra of sets, and so on. Coming from the EE background, I also know that you can…
artemonster
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Programmer struggling to navigate through mathematics notation and formulas(AI)

I'm a programmer and I've studied some calculus and linear algebra years ago. I've been getting in to AI recently and I struggle understanding some of the mathematical notation and formulas. I apologize ahead of time if my questions are stupid. In…
danial javady
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Finite State Automata

it's been a while since I've done FSA's so I'm a little rusty, bear with me. I'm creating an FSA to parse Integer and Decimal tokens for a class. The two tokens have the regex Integer: $0|[1-9][0-9]^*$\ Decimal:…
AFC
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Equivalence of NFA with and without $\epsilon$-transitions.

I am reading through the first edition of $\textit{Introduction to Automata Theory, Languages, and Computation}$ by Hopcroft and Ullman. They introduce the notions of NFA's and $\epsilon$-NFA's as follows. Fix a finite alphabet $\Sigma$. A…
Sprinkle
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How to derive a procedure to perform bitwise OR between two regular expressions

I was given this problem on regular languages, which I solved, but I was wondering there is another, more elegant way to approach it. I'll share the problem first, along with my solution, and then state how I first thought how to solve it - from…
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Can NFAs have infinitely many edges?

This question is about whether the definition of weighted Non-deterministic Finite state Automata (NFAs) excludes the possibility of infinitely many transitions. The definition of Finite State Automata implies finitely many states, with a finite…
languagen00b
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Counting the number of possible strings given some constraints

So this is more of a statement of an interesting approach I found (of solving a particular type of problem) than a question, but I would like to read up more on the subject, if there even is a subject here. So maybe that would be my question - where…
milin
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Probability from an Unknown State in a Finite State Machine

I'm attempting to model probability for a finite state machine. The probability of the next state depends on the current state. However, I'd like to handle the case where I don't know the starting state. Originally I just averaged all the output…
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How do I know if a base-$3$ number is congruent to $3\pmod 5$?

The problem: Professor Martinez needs a state machine that will recognize certain base-$3$ numbers. It should read the digits in left-to-right order. That is, if you’ve seen number $x$ and read a new digit $d$, your new number is $3x + d$. The…
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