Q:

Restart process on linux by its pidn number with kill command, how?

Well, I want to be able to restart processes on linux  and so I looked into kill manpages for that. Apparently kill -l would list all the signals I could send to a process to do what I need, which are: 
 1) SIGHUP       2) SIGINT       3) SIGQUIT      4) SIGILL       5) SIGTRAP
 6) SIGABRT      7) SIGBUS       8) SIGFPE       9) SIGKILL     10) SIGUSR1
11) SIGSEGV     12) SIGUSR2     13) SIGPIPE     14) SIGALRM     15) SIGTERM
16) SIGSTKFLT   17) SIGCHLD     18) SIGCONT     19) SIGSTOP     20) SIGTSTP
21) SIGTTIN     22) SIGTTOU     23) SIGURG      24) SIGXCPU     25) SIGXFSZ
26) SIGVTALRM   27) SIGPROF     28) SIGWINCH    29) SIGIO       30) SIGPWR
31) SIGSYS      34) SIGRTMIN    35) SIGRTMIN+1  36) SIGRTMIN+2  37) SIGRTMIN+3
38) SIGRTMIN+4  39) SIGRTMIN+5  40) SIGRTMIN+6  41) SIGRTMIN+7  42) SIGRTMIN+8
43) SIGRTMIN+9  44) SIGRTMIN+10 45) SIGRTMIN+11 46) SIGRTMIN+12 47) SIGRTMIN+13
48) SIGRTMIN+14 49) SIGRTMIN+15 50) SIGRTMAX-14 51) SIGRTMAX-13 52) SIGRTMAX-12
53) SIGRTMAX-11 54) SIGRTMAX-10 55) SIGRTMAX-9  56) SIGRTMAX-8  57) SIGRTMAX-7
58) SIGRTMAX-6  59) SIGRTMAX-5  60) SIGRTMAX-4  61) SIGRTMAX-3  62) SIGRTMAX-2
63) SIGRTMAX-1  64) SIGRTMAX

I thought that I would get the desired effect by using SIGSTOP signal (number 19) and then SIGCONT signal (number 18) like this:
kill -19 $PID_NUMBER # It stops! nice, we are reaching just what we wanted.
kill -18 $PID_NUMBER # Ok... it continues to death... that isn't funny though.

I also tried with signal number 1 : SIGHUP with pretty much the same results, am I missing something? Does anyone know what I need to reach what I want?

A:

There is no “restart” signal. You need to record the environment (environ, cwd, cmdline, security context…) from /proc/<pid> and manually start the process again.
SIGHUP is close, but it is only used by convention to ask the program to reload its settings.

