Assume that you have implemented the vector clock algorithm. However, some application needs Lamport's logical clock. Write a function convert that takes as input a vector timestamp and outputs a logical clock timestamp. Given an example to show where direct dependency clocks fail to capture causality. Modify Lamport's mutual exclusion algorithm to support reader-writer locks. That is, multiple con- current readers are OK as long there are no writers. Assume that you have implemented the vector clock algorithm. However, some application needs Lamport's logical clock. Write a function convert that takes as input a vector timestamp and outputs a logical clock timestamp. Given an example to show where direct dependency clocks fail to capture causality. Modify Lamport's mutual exclusion algorithm to support reader-writer locks. That is, multiple con- current readers are OK as long there are no writers