# Why cannot we reduce the Emptiness problem of LBA to the Acceptance problem of LBA?

I am a little bit confused about the emptiness problem of the linear bounded automaton (LBA). I know that this problem is undecidable. However if we assume that is decidable, what could be wrong if we reduce it to the acceptance problem of LBA?

• I'm not sure what you're trying to do. You don't need to assume that something is decidable before reducing it to something else. But, if you come up with a reduction from a problem A to a decidable problem B, you know that A is decidable; if you reduce an undecidable problem C to a problem D, you know that D is also undecidable. – David Richerby Mar 14 '17 at 9:02
• It seems I put it the other way, what I want to do is to reduce the acceptance problem of LBA to the emptiness problem of LBA giving that the acceptance problem is decidable and assuming that we have no idea whether the emptiness problem is decidable or not. The question is why we cannot do this? And if there is a way to do it then how? – O.S. Mar 14 '17 at 9:08
• Reducing a problem to another is a way of proving that one of the problems is or is not decidable. If you were to assume decidability in advance, you'd be assuming the thing you were trying to prove. – David Richerby Mar 14 '17 at 13:00