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This paper is on a brief interpretation of class P and NP in infinite Hamming cube consisting all the instances of any language in P or NP as well as all the instances of a Turing machine’s tape per configuration. It is shown that P and NP are more comparable when defined in Hamming space; while, this results P = NP.

This paper is on a brief interpretation of class P and NP in infinite Hamming cube consisting all the instances of any language in P or NP as well as all the instances of a Turing machine’s tape per configuration. It is shown that P and NP are more comparablewhen defined in Hamming space; while, this results P = NP.

This paper is on a brief interpretation of class P and NP in infinite Hamming cube consisting all the instances of any language in P or NP as well as all the instances of a Turing machine’s tape per configuration. It is shown that P and NP are more comparable when defined in Hamming space; while, this results P = NP.

This paper is on a brief interpretation of class P and NP in Hamming space. It is shown that P and NP are more comparablewhen defined in Hamming space; while, this results P = NP.

This paper is on a brief interpretation of class P and NP in Hamming space. It is shown that P and NP are more comparable when defined in Hamming space; while, this results P = NP.

This paper is on a brief interpretation of class P and NP in infinite Hamming cube consisting all the instances of any language in P or NP as well as all the instances of a Turing machine’s tape per configuration. It is shown that P and NP are more comparable when defined in Hamming space; while, this results P = NP.

This paper is on a brief interpretation of class P and NP in infinite Hamming cube consisting all the instances of any language in P or NP as well as all the instances of a Turing machine’s tape per configuration. It is shown that P and NP are more comparablewhen defined in Hamming space; while, this results P = NP.

This paper is on a brief interpretation of class P and NP in infinite Hamming cube consisting all the instances of any language in P or NP as well as all the instances of a Turing machine’s tape per configuration. It is shown that P and NP are more comparable when defined in Hamming space; while, this results P = NP.

This paper is on a brief interpretation of class P and NP in infinite Hamming cube consisting all the instances of any language in P or NP as well as all the instances of a Turing machine’s tape per configuration. It is shown that P and NP are more comparable when defined in Hamming space; while, this results P = NP.

This paper is on a brief interpretation of class P and NP in Hamming space. It is shown that P and NP are more comparablewhen defined in Hamming space; while, this results P = NP.

This paper is on a brief interpretation of class P and NP in Hamming space. It is shown that P and NP are more comparablewhen defined in Hamming space; while, this results P = NP.

This paper is on a brief interpretation of class P and NP as bounds over the number of jumps between strings in an infinite Hamming cube consisting all the instances of any language in P or NP as well as all the instances of a Turing machine’s tape per configuration. It is shown that P and NP are more comparable when defined in Hamming space respecting its cubic structure; while, this results P = NP.

We show that the feasibility of a booking in the European entry-exit gas market can be decided in polynomial time on single-cycle networks that are passive, i.e. do not contain controllable elements. The feasibility of a booking can be characterized by solving polynomially many nonlinear potential-based flow models for computing so-called potential-difference maximizing load flow scenarios. We thus analyze the structure of these models and exploit both the cyclic graph structure as well as specific properties of potential-based flows. This enables us to solve the decision variant of the nonlinear potential-difference maximization by reducing it to a system of polynomials of constant dimension that is independent of the cycle's size. This system of fixed dimension can be handled with tools from real algebraic geometry to derive a polynomial-time algorithm. The characterization in terms of potential-difference maximizing load flow scenarios then leads to a polynomial-time algorithm for deciding the feasibility of a booking. Our theoretical results extend the existing knowledge about the complexity of deciding the feasibility of bookings from trees to single-cycle networks., SCOPUS: ar.j, info:eu-repo/semantics/published