Deterministic finite automaton

Finite automata

In the theory of computation, a branch of theoretical computer science, a deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state automaton (DFSA)—is a finite-state machine that accepts or rejects a given string of symbols, by running through a state sequence uniquely determined by the string. Deterministic refers to the uniqueness of the computation run. In search of the simplest models to capture finite-state machines, Warren McCulloch and Walter Pitts were among the first researchers to introduce a concept similar to finite automata in 1943. The figure illustrates a deterministic finite automaton using a state diagram. In this example automaton, there are three states: S0, S1, and S2 (denoted graphically by circles). The automaton takes a finite sequence of 0s and 1s as input. For each state, there is a transition arrow leading out to a next state for both 0 and 1. Upon reading a symbol, a DFA jumps deterministically from one state to another by following the transition arrow. For example, if the automaton is currently in state S0 and the current input symbol is 1, then it deterministically jumps to state S1. A DFA has a start state (denoted graphically by an arrow coming in from nowhere) where computations begin, and a set of accept states (denoted graphically by a double circle) which help define when a computation is successful. A DFA is defined as an abstract mathematical concept, but is often implemented in hardware and software for solving various specific problems such as lexical analysis and pattern matching. For example, a DFA can model software that decides whether or not online user input such as email addresses are syntactically valid. DFAs have been generalized to nondeterministic finite automata (NFA) which may have several arrows of the same label starting from a state. Using the powerset construction method, every NFA can be translated to a DFA that recognizes the same language. DFAs, and NFAs as well, recognize exactly the set of regular languages. (Wikipedia).

9H The Determinant

Equivalent statements about the determinant.

From playlist Linear Algebra

9E The Determinant

General rules for the determinant.

From playlist Linear Algebra

Linear Algebra: Ch 2 - Determinants (1 of 48) What is a Determinant? (Part 1)

Visit http://ilectureonline.com for more math and science lectures! In this video I will give a general definition of “What is a Determinant?” (Part 1) Next video in this series can be seen at: https://youtu.be/vIHnlNjRnGU

From playlist LINEAR ALGEBRA 2: DETERMINANTS

9F The Determinant

Equivalent statements about the determinant.

From playlist Linear Algebra

9D The Determinant

A combinatorial approach to the determinant using permutations.

From playlist Linear Algebra

Determinant of an Operator and of a Matrix

Determinant of an operator. An operator is not invertible if and only if its determinant equals 0. Formula for the characteristic polynomial in terms of determinants. Determinant of a matrix. Connection between the two notions of determinant.

From playlist Linear Algebra Done Right

Cellular Automata Rule-Generating Polynomials

Cellular Automata rules are represented by integers where we encode the output of the function without knowing the details on how it might be implemented. The CellularAutomaton function in Mathematica only requires these integers, along with the values of r and k, to evolve rules for a giv

From playlist Wolfram Technology Conference 2022

Diego Figueira: Semistructured data, Logic, and Automata – lecture 1

Semistructured data is an umbrella term encompassing data models which are not logically organized in tables (i.e., the relational data model) but rather in hierarchical structures using markers such as tags to separate semantic elements and data fields in a ‘self-describing’ way. In this

From playlist Logic and Foundations

2.1 Finite State Automata

From playlist Information Service Engineering by Dr. Harald Sack and Dr. Maria Koutraki

Potential Automorphy for Compatible Systems of l-Adic Galois Representations - David Geraghty

David Geraghty Princeton University; Member, School of Mathematics November 18, 2010 I will describe a joint work with Barnet-Lamb, Gee and Taylor where we establish a potential automorphy result for compatible systems of Galois representations over totally real and CM fields. This is ded

From playlist Mathematics

9C The Determinant

More on properties of determinant.

From playlist Linear Algebra

History of Science and Technology Q&A (November 30, 2022)

Stephen Wolfram hosts a live and unscripted Ask Me Anything about the history of science and technology for all ages. Find the playlist of Q&A's here: https://wolfr.am/youtube-sw-qa Originally livestreamed at: https://twitch.tv/stephen_wolfram If you missed the original livestream of thi

From playlist Stephen Wolfram Ask Me Anything About Science & Technology

4. Pushdown Automata, Conversion of CFG to PDA and Reverse Conversion

MIT 18.404J Theory of Computation, Fall 2020 Instructor: Michael Sipser View the complete course: https://ocw.mit.edu/18-404JF20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60_JNv2MmK3wkOt9syvfQWY Quickly reviewed last lecture. Defined context free grammars (CFGs) a

From playlist MIT 18.404J Theory of Computation, Fall 2020

Quasicrystal Phases in a Finite-Range Lattice Gas Model - Siamak Taati

From playlist Mathematics of Condensed Matter and Beyond (February 22-25, 2021)

Pierre-Alain Reynier : Transductions - Partie 2

Résumé : Après une introduction générale présentant les principaux modèles et problèmes étudiés, nous étudierons plus précisément trois sujets qui permettront d’illustrer des propriétés algorithmiques, des aspects algébriques et logiques de cette théorie : - caractérisation, décision et mi

From playlist Logic and Foundations

Émilie Charlier: Logic, decidability and numeration systems - Lecture 1

Abstract: The theorem of Büchi-Bruyère states that a subset of Nd is b-recognizable if and only if it is b-definable. As a corollary, the first-order theory of (N,+,Vb) is decidable (where Vb(n) is the largest power of the base b dividing n). This classical result is a powerful tool in ord

From playlist Mathematical Aspects of Computer Science

Emmanuel Filiot : Transductions - Partie 1

From playlist Logic and Foundations

Finite State Automata

A recap of the week's lectures about Finite State Automata. Converted to/from regular expressions.

From playlist Discrete Structures

2. Nondeterminism, Closure Properties, Conversion of Regular Expressions to FA

From playlist MIT 18.404J Theory of Computation, Fall 2020

Group automorphisms in abstract algebra

Group automorphisms are bijective mappings of a group onto itself. In this tutorial I define group automorphisms and introduce the fact that a set of such automorphisms can exist. This set is proven to be a subgroup of the symmetric group. You can learn more about Mathematica on my Udem

From playlist Abstract algebra

Deterministic finite automaton

Related pages