Presburger arithmetic is the first-order theory of the natural numbers with addition, named in honor of Moj¿esz Presburger, who introduced it in 1929. The signature of Presburger arithmetic contains only the addition operation and equality, omitting the multiplication operation entirely. The axioms include a schema of induction. Presburger arithmetic is much weaker than Peano arithmetic, which includes both addition and multiplication operations.
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Termination analysis
In computer science, a termination analysis is program analysis which attempts to determine whether the evaluation of a given program will definitely terminate. Because the halting problem is undecidable, termination analysis cannot work correctly in all cases. The aim is to find the answer "program does terminate" (or "program does not terminate") whenever this is possible.
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Program optimization
In computer science, program optimization or software optimization is the process of modifying a software system to make some aspect of it work more efficiently or use fewer resources. In general, a computer program may be optimized so that it executes more rapidly, or is capable of operating with less memory storage or other resources, or draw less power.
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Arithmetic
Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of operations that combine numbers. In common usage, it refers to the simpler properties when using the traditional operations of addition, subtraction, multiplication and division with smaller values of numbers.
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Computer program
A computer program (also software, or just a program) is a sequence of instructions written to perform a specified task with a computer. A computer requires programs to function, typically executing the program's instructions in a central processor. The program has an executable form that the computer can use directly to execute the instructions.
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Inference
Inference is the act or process of deriving logical conclusions from premises known or assumed to be true. The conclusion drawn is also called an idiomatic. The laws of valid inference are studied in the field of logic. Human inference (i.e. how humans draw conclusions) is traditionally studied within the field of cognitive psychology; artificial intelligence researchers develop automated inference systems to emulate human inference.
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