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The problem whether there exists an algorithm recognizing inference rules admissible in TS4 is a long-standing open problem.
That is, there exists an algorithm A which is able to obtain the secret a from H a)⊕b and H a)⊕c within the polynomial-time.
By the contradiction proof, assume that there exists an algorithm A can obtain the value H(a) from H a)⊕b and H a)⊕c within a polynomial-time.
Specifically, there exists an algorithm with complexity of that guarantees the finding of the optimal solution, however its high complexity limits its applicability for real-time computations and can be used only for benchmarking purposes.
Thus if there exists an algorithm to solve an arbitrary diophantine equation of degree increasing type, then it can solve an arbitrary diophantine equation, which contradicts Matijasevič's result [10].
We say that an algorithmic problem A is as hard as an algorithmic problem B if for any decision algorithm for A which solves the problem in time (T_{A}) there exists an algorithm for B that solves it in time (preccurlyeq T_A).
Similar(51)
A system which is apparently but not sensitively dependent on initial conditions will be unpredictable to us, but there will exist an algorithm that, given some finite specification of the initial conditions, generates the future evolution of the system perfectly.
Computability: there exists an efficient algorithm to calculate e u,v), for all u,v∈G. .
As the authors show in [8, Theorem 1] for the case of and receivers, there exists an offline algorithm that is both rate optimal and delay-free.
In this paper, we provide a proof that the problem is indeed NP-hard, so it is not likely that there exists an efficient algorithm that solves the problem optimally.
It may thus come as a surprise that there exists an adaptive algorithm for blind channel estimation [48, 49] that is indeed robust [46, 50], although it is known that most of the blind methods are non-robust [51]; see Algorithm 10 for details.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com