# P-complete problem due to logspace reductions. What does it mean?

Prove that problem $A$ is complete in $P$ due to reductions computed in logarythmic space

How to understand this statement ? What should be shown ? For me:
1. $A$ is in $P$.
2. Each problem in $P$ can be reduced in logspace to $A$

Can I use transitivity of logspace in this exercise ?

• Your understanding of the definition of "complete with respect to reductions computed in logarithmic space" is correct. – Yuval Filmus Aug 13 '17 at 3:15
• As to your other question, whether you can use transitivity of logspace in this exercise, this is a question to whoever gave you the exercise; we cannot possibly answer it. In published math you are allowed (and encouraged) to use whatever correct facts you can cite. – Yuval Filmus Aug 13 '17 at 3:16
• Question contains complete answer; voting to close. – Yuval Filmus Aug 13 '17 at 3:17
• @YuvalFilmus I meant: Can I use trick similar to logspace transitivity ? Some machine $C$ capture readings from tape (field $i$) of machine $K$ and in logspace provides field $i$. So the difference is that here $K$ works in $P$, no logspace. Is it also ok in this case use this trick ? – Haskell Fun Aug 13 '17 at 7:01
• You need to give a logspace reduction from a P-complete problem (with respect to logspace reductions) to A. – Yuval Filmus Aug 13 '17 at 12:55