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In the state-transition table, all possible inputs to the finite-state machine are enumerated across the columns of the table, while all possible states are enumerated across the rows. If the machine is in the state S 1 (the first row) and receives an input of 1 (second column), the machine will stay in the state S 1 .
A transition without consuming an input symbol is called an ε-transition and is represented in state diagrams by an arrow labeled "ε". ε-transitions provide a convenient way of modeling systems whose current states are not precisely known: i.e., if we are modeling a system and it is not clear whether the current state (after processing some ...
State diagram for a turnstile A turnstile. An example of a simple mechanism that can be modeled by a state machine is a turnstile. [4] [5] A turnstile, used to control access to subways and amusement park rides, is a gate with three rotating arms at waist height, one across the entryway.
While this is the most common definition, some authors use the term deterministic finite automaton for a slightly different notion: an automaton that defines at most one transition for each state and each input symbol; the transition function is allowed to be partial. [5] When no transition is defined, such an automaton halts.
It can manipulate the stack as part of performing a transition. A pushdown automaton reads a given input string from left to right. In each step, it chooses a transition by indexing a table by input symbol, current state, and the symbol at the top of the stack. A pushdown automaton can also manipulate the stack, as part of performing a transition.
The table column "Current Rules" documents the meaning and syntax possibilities for each state, as worked out by the parser generator. It is not included in the actual tables used at parsing time. The • (pink dot) marker shows where the parser is now, within some partially recognized grammar rules.
Each transition edge is labeled with the value of the input (shown in red) and the value of the output (shown in blue). The machine starts in state S i . (In this example, the output is the exclusive-or of the two most-recent input values; thus, the machine implements an edge detector, outputting a 1 every time the input flips and a 0 otherwise.)
Given a DFA, the problem of determining if it has a synchronizing word can be solved in polynomial time [2] using a theorem due to Ján Černý. A simple approach considers the power set of states of the DFA, and builds a directed graph where nodes belong to the power set, and a directed edge describes the action of the transition function.