DetermineSISO Decision Problem

Hemani Alaparthi, Hannah Brown, Issei Hasegawa

September 8, 2025

Introduction

• SISO = Single Input, Single Output → input processed → one output

• Why it matters: Predictability, correctness, and links to the Halting Problem

Keep in mind halting detector. Halting detector tells if a program would stop or run forever.

Problem

• Undecidability No algorithm can always decide whether a program halts (the Halting Problem) → SISO is undecidable.

• All-input guarantee The input domain is infinite, so finite testing can’t prove a program halts with exactly one output for all inputs.

• Trade-off In restriction (no loops/recursion), we can verify SISO by checking the code (static analysis).

Static analysis is reasoning about a program’s behavior just by looking at its code, not by executing it.

Theory Insights

• ∀ vs ∃: To prove SISO we need ∀ inputs → impossible by testing.
  
• Type hints ≠ guarantees: Annotations show intent, not behavior.
  
• Checker reality: We can detect some violations (NO), but a universal YES is impossible.
  
• Restrictions help: In loop-free / recursion-free languages, static analysis can decide SISO.

Python Implementation

Example Solution

• Built a tool: DetermineSISO
  
• Runs a target program on a finite set of test inputs
  
• Checks for:
  • Halting within a timeout
    
  • Exactly one line of output
    
• Verdicts:
  • ✅ SISO-LIKELY
    
  • ❌ NOT-SISO-LIKELY
    
  • ❓ INDETERMINATE

Example Target

✅ Halts with one output

def main(s: str) -> str:
    return "OK"

❌ Infinite loop (non-SISO)

def main(s: str) -> str:
    while True:
        pass

Output:

$ python determine_siso.py siso_ok.py --autogen-inputs 5
SISO-LIKELY on tested inputs ✅

$ python determine_siso.py not_siso.py --autogen-inputs 3 --timeout 0.5
NOT-SISO-LIKELY on tested inputs ❌

Limitations

• Bounded testing → Only covers finite inputs, not all inputs

• Timeouts → A loop might pass if it halts just within the limit

• False positives → Program may fail on untested inputs

Conclusion

• In general, it is impossible to realize DetermineSISO as a verifier that always returns a correct Yes/No.
• SISO is a non-trivial semantic property; due to the Halting Problem, no algorithm can fully decide it automatically for arbitrary programs.
• DetermineSISO works heuristically, but a perfect verifier is impossible (Halting Problem).