Matching decompilation is a verifiable target that ensures feature parity but it says nothing about being reasonable non slop decompilation.
Disassembler output can relatively easily match original binary, I doubt anyone would consider it decompilation.
Let's say you add requirement of being higher abstraction language than assembly. You can translate the assembly code 1:1 with simple string substitions to C code which would provably replicate the behavior of program perfectly. I would consider that more of hard coded emulation, opposite of JIT like ahead of time code translation. Just because the intermediate langauge is higher level language than assembly doesn't automatically mean that the program text operates at higher level of abstraction than assembly.
I have seen plenty of decompilation projects where you start reading the code many functions contain nonsensical variable reuse (and name that match the register names), address calculations and memory casts and array calculations, arrays of function pointers, offsets within structures which strongly mirrors the assembly code.
The problem is that you can't draw a hard line how good do the variable/function names need to be so that it can be considered decompilation instead of hard coded emulation. It's hard to draw a line for how much of higher level language features you need to use to be considered decompilation. It's hard to define how logical the control flow needs to be. The line becomes blurrier by system programmers approaching it from the other side. Sometimes an extensively optimized code can contain a lot more manual memory mangling, index and offset calculations, manual unrolling than the language requires. So many C programs with homebrew systems of emulating virtual functions using structs of pointers. In such situations it's hard to tell if decompilation is incomplete or whether program was written that way from start.
Another possibility of junk decompilation (which perfectly compiles to byte identical copy of original executable) is program which depends on exact program layout in memory or undefined aspects of programming language. It would perfectly replicate original behavior on original hardware/compiler, but provide 0 insights in intended program behavior and fail miserably when attempting to modify the code or port it to different hardware/compiler. For example the "decompiled" code might intentionally peform out of bounds array access thus touching completely different variable or depend on fallthrough between functions lacking return statement.
Taking it to the extreme would be something like:
```
char data[] = {0x10, 0x12, 0xab, 0xcf, ...}; // bytes corresponding to majority of original program.
int main(){
((void*())data)(); // cast the array to function pointer and execute it
}
```
It might behave exactly like original program, but that's junk decompilation.
You could add additional restriction that C program isn't allowed to exploit any undefined or machine specific behavior, but then there is very high chance that even original program wouldn't satisfy it.
Original program might also contain parts of it written in assembly for performance reasons or because that was only way to access certain hardware features. What does it mean for decompilation? Is decompiled code not allowed to use the same techniques. If decompiled code is allowed to have some pieces of assembly what stops it from using it for everything. There is no way of knowing precisely how much assembly the original program used.