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A functionally complete logic system may be composed of relays, valves (vacuum tubes), or transistors. Electronic logic gates differ significantly from their relay-and-switch equivalents. They are much faster, consume much less power, and are much smaller (all by a factor of a million or more in most cases).
Diagrammatic representation of computer logic gates. Logic in computer science covers the overlap between the field of logic and that of computer science. The topic can essentially be divided into three main areas: Theoretical foundations and analysis; Use of computer technology to aid logicians; Use of concepts from logic for computer applications
In proof complexity, a Frege system is a propositional proof system whose proofs are sequences of formulas derived using a finite set of sound and implicationally complete inference rules. [1] Frege systems (more often known as Hilbert systems in general proof theory ) are named after Gottlob Frege .
The 3-input Fredkin gate is functionally complete reversible gate by itself – a sole sufficient operator. There are many other three-input universal logic gates, such as the Toffoli gate. In quantum computing, the Hadamard gate and the T gate are universal, albeit with a slightly more restrictive definition than that of functional completeness.
In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of a system with respect to a certain formal specification or property, using formal methods of mathematics. [1] Formal verification is a key incentive for formal specification of systems, and is at the core of formal methods.
Logic simulation is the use of simulation software to predict the behavior of digital circuits and hardware description languages. [ 1 ] [ 2 ] Simulation can be performed at varying degrees of physical abstraction , such as at the transistor level , gate level , register-transfer level (RTL), electronic system-level (ESL), or behavioral level.
Boolean circuits are defined in terms of the logic gates they contain. For example, a circuit might contain binary AND and OR gates and unary NOT gates, or be entirely described by binary NAND gates. Each gate corresponds to some Boolean function that takes a fixed number of bits as input and outputs a single bit.
A proof procedure for a logic is complete if it produces a proof for each provable statement. The theorems of logical systems are typically recursively enumerable, which implies the existence of a complete but usually extremely inefficient proof procedure; however, a proof procedure is only of interest if it is reasonably efficient.