How is “δ: Q × Σ → Q” read in the definition of DFA (deterministic finite state machine)?

Question

How do you say δ: Q × Σ → Q in English? Describing what the meanings of × and → mean will also help.

Answer 1

δ is similar to a mathematical function called the transition function. Something like.

 z = f(x, y) 

A function in mathematics determines the mapping of elements in one set to another set. The function set of input arguments is called Domain of function, and the output is fury.

[ANSWER]

In the expression "δ:Q×Σ → Q" ,

× means a Cartesian product (this is a set), and → is a mapping .
> "δ:Q×Σ → Q" says that δ is a transition function that defines a mapping from Q×Σ to Q Where, the region δ is Q × Σ , and Range is Q

Note: A Cartesian product in itself is mathematical, that all possible pairs (mapping) are between two sets.

You can also say:

δ is the transition function that determined the mapping between (or, say, associates) the Cartesian product of the set of states Q and the language symbols Σ into the set of states Q This is abbreviated as δ: Q × Σ → Q

Here Q is a finite set of states, and Σ is a finite set of language symbols.

In addition, in any automatic mode, you can present the transition function in the form of a tree.
1. Transition table
2. Transition graph or indicate a state diagram.
3. Transition function : a finite set of display rules. for example { δ(q0, a) → q1 , δ(q1, a) → q2 }
_{Everything for this purpose defines maping.}

In the DFA. δ:Q×Σ → Q can also be written as δ(Q,Σ) → Q It looks like a function. In the function δ two input arguments are the state Q and the language symbol Σ , and the return value is Q

What does δ(Q,Σ) → Q mean δ(Q,Σ) → Q

Suppose that in your set of transition function δ you have an element δ(q0, a) → q1 . If the current state is q0 , then by consuming the symbol a , you can go to state q1 . And the state diagram for δ(q0, a) → q1 :

 (q0)---a---►(q1) 

and transition table :

 +----+----+ |Q\Σ | a | +----+----+ | q0 | q1 | +----+----+ 

and everything determines the map (q0, a) to (q1) .

Some authors write δ ⊆ Q×Σ → Q in the formal definition of DFA, which means that δ is a partial function (not defined for the complete domain Q×Σ ). We can always determine δ in the full domain that was once needed, for example, to look for a DFA add-on. Here ( DFA Supplement ) I wrote two DFAs for the same language, one of which is a partial DFA and the other DFA add-on.

Answer 2

Sorry if the conditions are not entirely correct (in English). I study car theory about 3 or 4 years ago in another language, so the terms may not be entirely accurate.

δ is similar to a partial function with two arguments, which takes as the input state (this is the state of the automaton, element Q) and the "input action" (element Σ, which is the alphabet accepted by the automaton *), and produces a new state that the automaton must have after providing them with an input action.

This can basically be read as:

delta transition function defined on the Q-set of states of the automaton and sigma alphabet

× in the formula represents the Cartesian product of states and sets of actions, and → means that what is returned by the function belongs to the next one (in your case, Q).

* should not be confused with the language adopted by the automaton, which will be all sequences of “input actions” that have valid transitions (ie, δ (stateX, input)) and bring the automaton to its final “acceptable” state.

Answer 3

Cue Sigma to Cue Delta

or

Transition function, delta that displays ordered pairs of states and input characters, sigma blue case, states, cue.

Answer 4

Easy to quote from Wikipedia :

δ - state transition table: I would read "×" as a table and "→" as entries in this table.

Then in natural language: indicate what state (element Q) will be received if the machine is in the specified state and sees a certain character (element from Σ).