Multi-user CRUD: Valid, Problem, or Error?

JavaScript (ES6), 36 bytes

Without a lookup table

(m,a,f,A,F)=>f-F?2:a^A?a*A&8:a&4?m:a

Try it online!

I/O

• Locking mode (\$m\$): \$0\$ = On, \$8\$ = Off
• Actions (\$a\$ and \$A\$): \$0\$ = Create, \$2\$ = Read, \$4\$ = Update, \$8\$ = Delete
• Files (\$f\$ and \$F\$): any integers
• Output: \$0\$ = Error, \$2\$ = Valid, \$8\$ = Problem

How?

If the files are different, all operations are safe and we just return \$2\$ (valid).

If the files are identical, we need to return:

• \$2\$ (valid) if we have two read operations
• \$8\$ (problem) if we have two delete operations, or one update and one read
• \$m\$ (either problem or error) if we have two update operations
• \$0\$ (error) for everything else

Using a \$4\times4\$ CRUD matrix (which is symmetric by definition), we can see that the above values can be computed with:

$$\underbrace{\text{a ^ A}}_{a\neq A?}\text{ ? }\color{blue}{\text{a * A & 8}}\text{ : }\underbrace{\text{a & 4}}_{\text{update?}}\text{ ? }\color{red}{\text{m}} : \color{magenta}{\text{a}}$$

$$\begin{array}{cc|cccc} &&\text{C}&\text{R}&\text{U}&\text{D}\\ &&0&2&4&8\\ \hline \text{C}&0&\color{magenta}{0}&\color{blue}{0}&\color{blue}{0}&\color{blue}{0}\\ \text{R}&2&\color{blue}{0}&\color{magenta}{2}&\color{blue}{8}&\color{blue}{0}\\ \text{U}&4&\color{blue}{0}&\color{blue}{8}&\color{red}{\text{m}}&\color{blue}{0}\\ \text{D}&8&\color{blue}{0}&\color{blue}{0}&\color{blue}{0}&\color{magenta}{8} \end{array}$$

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JavaScript (ES6),  46 45  40 bytes

With a lookup table

(m,a,f,A,F)=>f-F?0:[m,1,1,0][a*2+A*9&23]

Try it online!

I/O

• Locking mode: undefined = On, \$1\$ = Off
• Actions: \$0\$ = Update, \$1\$ = Read, \$2\$ = Create, \$3\$ = Delete
• Files: any integers
• Output: undefined = Error, \$0\$ = Valid, \$1\$ = Problem

Retina 0.8.2, 53 bytes

^(.)(?!\1).+|..RR.
V
..DD.
P
..UUL
E
.+[CD].+
E
..+
P

Try it online! Link includes test suite. Takes input as a string of 5 characters, two characters representing the file names, then two characters from CRUD, then L or U (locked/unlocked), and outputs one of VPE (valid/problem/error). Explanation:

^(.)(?!\1).+|..RR.
V

Different file names are always valid, as are two reads. Annoyingly, this is the only test that forces me to use a header. (It would cost an extra byte to make the header unnecessary.)

..DD.
P

Two deletes are always a problem.

..UUL
E

Two locked updates are an error.

.+[CD].+
E

Any other creates or deletes are an error.

..+
P

Everything else is a problem.

Octave, 96 bytes

@(a,b,c)[a(1)!=b(1)|a(2)+b(2)==20,mod((m=a+b+c)(2),10010)<1|mod(m(2),1020000)<1|mod(m(2),200)<1]

Try it online!

Definitely can be shorter, but I don't have time right now to do that

File 1 = 0
File 2 = 1
Read = 10
Delete = 100
Create = 1000 
Update = 10000
Lock on = 100000
Lock off = 1000000

Valid Values: 
[1 0] 

Problem Values: 
[0 1]


Invalid Values: 
[0 0]

Input as a = [file, action], b = [file2, action2], c = lock