Problem $1.$ Transaction management. Ri$($x$)$ refers to transaction Ti reading item x and Wj$($y$)$ refers to transaction Tj writing item y$.$ For each schedule below:

a$)$ S$1$: R$1($x$)$ R$1($y$)$ R$2($y$)$ R$2($x$)$ W$1($z$)$ W$2($z$)$ W$1($x$)$ W$2($y$)$

b$)$ S$2$: R$1($x$)$ R$2($y$)$ R$2($x$)$ W$2($z$)$ W$1($x$)$ W$1($z$)$ W$2($y$)$

$[20+20$ points$]$ Prove whether or not it is conflict serializable

$[10+10$ points$]$ If it is serializable write down an equivalent serial schedule. If it is not serializable explain why not

Problem $2.[20+20$ points$]$ Assuming the $2$PL protocol is in place, prove the presence$/$absence of deadlocks for each one of the previous schedules