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I need to prove that the following problem $0$-$1$ $\mathsf{ Ineq}$ is $\mathsf{NL}$-complete.

Given a finite set of variables $V$, a finite set of inequalities of the form $x \le y$ (where $x, y \in V$) and a finite set of equalities of the form $x=a$ (where $x \in V$ and $a \in \{0,1\}$), is there an assignment of values from $\{0, 1\}$ to the variables satisfying all the inequalities and all the equalities?

How can I start to resolve the proof?

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  • $\begingroup$ A start: what are the two things you need to show when you want to prove something is NL-complete? $\endgroup$
    – Juho
    Feb 21, 2013 at 23:32

2 Answers 2

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Hint: Directed reachability is NL-complete.

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Hint: This is 2SAT in disguise.

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