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A bank is a financial institution that accepts deposits from the public and creates a demand deposit while simultaneously making loans. Lending activities can be directly performed by the bank or indirectly through capital markets. Whereby banks play an important role in financial stability and the economy of a country, most jurisdictions exercise a high degree of regulation over banks. Most countries have institutionalized a system known as fractional-reserve banking, under which banks hold liquid assets equal to only a portion of their current liabilities.
In computational complexity theory, a problem is NP-complete when: It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no". When the answer is "yes", this can be demonstrated through the existence of a short (polynomial length) solution. The correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions.
In computational complexity theory, NP-hardness (non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard problem is the subset sum problem. A more precise specification is: a problem H is NP-hard when every problem L in NP can be reduced in polynomial time to H; that is, assuming a solution for H takes 1 unit time, Hs solution can be used to solve L in polynomial time.
In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems. NP is the set of decision problems for which the problem instances, where the answer is "yes", have proofs verifiable in polynomial time by a deterministic Turing machine, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine. NP is the set of decision problems solvable in polynomial time by a nondeterministic Turing machine.
A central bank, reserve bank, or monetary authority is an institution that manages the currency and monetary policy of a country or monetary union. In contrast to a commercial bank, a central bank possesses a monopoly on increasing the monetary base. Many central banks also have supervisory and/or regulatory powers to ensure the stability of commercial banks in their jurisdiction, to prevent bank runs, and in some cases also to enforce policies on financial consumer protection and against bank fraud, money laundering, or terrorism financing.