However, we observe that HTML lexers converge to a stable, recurring state after a small number kof characters. The state S5 recognizes S T a g and S3 does E T a g and S6 does C on t ent.Īs well as other FSM problem, lexing is inherently sequential processing in that the current state is based on the previous state. The convention is that unspecified transitions from accepting states behave as transitions from initial state. Then, we can draw a state transition diagram shown in figure 5.
![finite state automata lexer finite state automata lexer](http://quex.sourceforge.net/images/lexical-analysis-process.png)
(1 ) (3 ) Define th e sta t es, inpu t s and th e t r ansitions :We define the system with seven states denoted and define the transition based on the specification. We need to identify each lexeme from input string in the documents based on the HTML tag specifications. Struct branch *b = & the_table Ĭonsider we are lexing HTML documents. For example, figure 1 depicts state transition diagram where Q= įSM can be described as a state transition diagram. In order to solve this problem, it is natural to define set of states and the transition between them based on the lexical specification.įinite State Machine is defined formally as a 5‐tuple, ( Q, Σ, T, q 0, F) consisting of a finite set of states Q ,a finite set of input symbols Σ, a transition function T: Q x Σ → Q, an initial state q 0 ∈ Q, and final states F ⊆ Q. A current state is determined by past states of the system and many problems are expressed in terms of finite state machine such as control applications, compilers, lexers, speech recognition or string matching.įor example, in lexing HTML, input string and lexical specifications are given and we have to find lexemes.
![finite state automata lexer finite state automata lexer](https://i.stack.imgur.com/5V7we.jpg)
How can we efficiently represent this problem? Contextįinite state machine (FSM) allows for the concept of history, which is referred to as a state.
![finite state automata lexer finite state automata lexer](https://mitosystems.com/wp-content/uploads/2013/02/StateTransition.png)
Many problems take a sequence of input events (or string) and map it to a sequence of actions or output events (or string).