State (computer science)

In computer science and automata theory, the state of a digital logic circuit or computer program is a technical term for all the stored information, at a given instant in time, to which the circuit or program has access.^[1] The output of a digital circuit or computer program at any time is completely determined by its current inputs and its state.

Digital logic circuit state

Digital logic circuits can be divided into two types: combinational logic, whose output signals are dependent only on its present input signals, and sequential logic, whose outputs are a function of both the current inputs and the past history of inputs.^[2] In sequential logic, information from past inputs is stored in electronic memory elements, such as flip-flops and latches. The stored contents of these memory elements, at a given point in time, is collectively referred to as the circuit's state and contains all the information about the past to which the circuit has access.^[3]

For example, the state of a microprocessor is the contents of all the memory elements in it: the accumulators, storage registers, data caches, and flags. When computers such as laptops go into a hibernation mode to save energy by shutting down the processor, the state of the processor is stored on the computer's hard disk, so it can be restored when the computer comes out of hibernation, and the processor can take up operations where it left off.

Since each binary memory element, such as a flip-flop, has only two possible states, "one" or "zero", and there is a finite number of memory elements, a digital circuit has only a certain finite number of possible states. If N is the number of binary memory elements in the circuit, the maximum number of states a circuit can have is 2^N.

Program state

Similarly, a computer program stores data in variables, which represent storage locations in the computer's memory. The contents of these memory locations, at any given point in the program's execution, is called the program's state.^[4]^[5]^[6]

Imperative programming is a programming paradigm (way of designing a programming language) that describes computation in terms of the program state and statements that change the program state. In contrast, in declarative programming languages the program describes the desired results, and doesn't specify changes to the state directly.

A more specialized definition of state is used in some computer programs that operate serially (sequentially) on streams of data, such as parsers, firewalls, communication protocols and encryption programs. Serial programs operate on the incoming data characters or packets sequentially, one at a time. In some of these programs, information about previous data characters or packets received is stored in variables and used to affect the processing of the current character or packet. This is called a "stateful protocol" and the data carried over from the previous processing cycle is called the "state". In others, the program has no information about the previous data stream and starts "fresh" with each data input; this is called a "stateless protocol".

Finite state machines

The output of a sequential circuit or computer program at any time is completely determined by its current inputs and current state. Since each binary memory element has only two possible states, 0 or 1, the total number of different states a circuit can assume is finite, and fixed by the number of memory elements. If there are N binary memory elements, a digital circuit can have at most 2^N distinct states. The concept of state is formalized in an abstract mathematical model of computation called a finite state machine, used to design both sequential digital circuits and computer programs.

Types of states

Following states are distinguished:

Compatible states are states in a state machine that do not conflict for any input values. Thus for every input, both states must have the same output, and both states must have the same successor (or unspecified successors), or both must not change. Compatible states are redundant, if occurring in the same state machine.
Distinguishable states are states in a state machine that have at least one input sequence causing different output sequences - no matter which state is the initial state.
Equivalent states are states in a state machine which, for every possible input sequence, the same output sequence will be produced - no matter which state is the initial state.

References

↑ Harris, David Money; Sarah L. Harris (2007). Digital Design and Computer Architecture. USA: Morgan Kaufmann. p. 103. ISBN 0123704979.
↑ Kaeslin, Hubert (2008). Digital Integrated Circuit Design: From VLSI Architectures to CMOS Fabrication. UK: Cambridge University Press. p. 735. ISBN 0521882672.
↑ Srinath, N. K. (August 2005). 8085 Microprocessor: Programming and Interfacing. Prentice-Hall of India Pvt. Ltd. p. 326. ISBN 978-8120327856. Retrieved 7 December 2012. page 46
↑ Laplante, Philip A. (2000). Dictionary of Computer Science, Engineering and Technology. USA: CRC Press. p. 466. ISBN 0849326915.
↑ Misra, Jayadev (2001). A Discipline of Multiprogramming: Programming Theory for Distributed Applications. Springer. p. 14. ISBN 0387952063.
↑ Prata, Stephen Prata (2004). C Primer Plus, 5th Ed. Pearson Education. pp. 113–114. ISBN 0132713608.

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