A probabilistic Turing machine is a Turing machine whose transitions may depend on independent random bits.
A randomized decision algorithm has one-sided error when one answer is always correct and only the other answer can be mistaken.
contains decision problems with a polynomial-time randomized algorithm that rejects every negative instance and accepts every positive instance with probability at least one half.
consists of complements of languages in RP. Its algorithms always accept positive instances and reject negative instances with probability at least one half.
. Equivalently, it consists of problems having an always-correct randomized algorithm with polynomial expected running time.
Independent repetitions reduce a randomized algorithm's error probability while preserving polynomial running time.
Polynomial identity testing asks whether a polynomial represented implicitly, such as by an arithmetic circuit or a remainder computation, is the zero polynomial.
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An algorithm is a finite sequence of well-defined instructions or steps designed to perform a specific task or solve a particular problem. Algorithms can be expressed in various forms, including natural language, pseudocode, flowcharts, or programming code. Key characteristics of algorithms include: 1. **Clear and Unambiguous**: Each step must be precisely defined so that there is no uncertainty about what is to be done.
