The beauty of Mathematics 12th Chapter finite state machine-the core technology of map and local search __ The beauty of mathematics

Smart phone positioning and navigation capabilities, in fact, only three key technologies:

First, the use of satellite positioning

Second, the identification of the address

Third, according to user input to start and end, on the map to plan the shortest route or the fastest route
1 Address analysis and finite state machine

Address identification and analysis is an essential technology for local search.

The grammar of the address is a relatively simple one in the context-related grammar, so there are many methods of identification and analysis, but the most effective is the finite state machine.

A finite state machine is a special, forward graph that includes some States (nodes) and a forward arc connecting those states.

Each finite state machine has a start state and a termination state, as well as a number of intermediate states. Each arc has a condition that enters the next state from one state.

Using a finite state machine to identify the address, the key to solve two problems: the state machine through a number of limited addresses, and given a finite state machine, the address string matching algorithm.

Problem: When a user enters an address that is not standard or has a typo, the limited state opportunity is helpless because it can only be matched strictly. To solve this problem, we want to see the possibility of a fuzzy match and a string as the correct address. In order to achieve this goal, the scientists proposed a finite state machine based on probability. The finite state machine based on probability and the discrete Markov chain are basically equivalent.
2 Global navigation and dynamic planning

Can be a "search for the shortest route" problem, decomposed into a local shortest route small problem. As long as the crosscutting line from Beijing to Guangzhou, until Guangzhou, we have the shortest route to find. This is the principle of dynamic planning.
3 finite state sensors

The application of finite state machine is much more than the recognition of address, today's speech recognition encoder is basically based on the principle of finite state machine.

Finite state machines play a very important role in speech recognition and natural language understanding, but these fields use a special finite state machine-weighted finite state sensor (weighted finite states transducer, referred to as WFST)

The particularity of the finite state sensor (finite states transducer) is that each state in the finite state machine is defined by the input and output symbols.

Each path in the WFST is a candidate sentence in which the most probable path is the recognition result of the sentence.