Monitors are added upon problematic siphons to avoid deadlocks. Li and Zhou add monitors to elementary siphons only while controlling the rest dependent siphons to save cost. After failing a Marking Linear Inequality (MLI) test, they perform a Linear Integer Programming (LIP) test (NP-hard). We proposed a new MLI test earlier to avoid the LIP and extended it to S3PGR2 (systems of simple sequential processes with general resource requirements) for strongly dependent siphons (SDS). The control policy for weakly dependent siphons (WDS) is rather conservative due to some negative terms in the MLI. This paper shows that WDS and SDS have the same controllability (i.e., MLI). As a result, the control for WDS needs no longer be that conservative. We also develop an optimization (by redundancy elimination) of the computation required for LIP test to ensure deadlock prevention of S3PR (Systems of Simple Sequential Processes with Resources). A favorable result for this policy is that any n-dependent (n>2) WDS (similar to SDS) needs no monitor and hence the complexity for synthesizing a controller becomes polynomial.