Let G be a color graph where each node has a color and multiple nodes can share the same color. In particular, there is a designated initial node. An ω-path is an infinite walk on G that starts from the initial. A good ω- path is is one where there are infinitely many prefixes, each of which satisfies the following condition: the number of red nodes equals the number of blue nodes. Design an algorithm to decide whether there is a good ω-path

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