Work

P ≠ PSPACE: A Proof via Resource-Constrained Complexity Function Analysis

Year: 2025

Type: article

Abstract: We prove that P ≠ PSPACE by analyzing the fundamental structural differences between time-bounded and space-bounded computation. Using an extension of complexity function analysis, we demonstrate that P algorithms exhibit inherent computational limitations that create discontinuous complexity functions, while PSPACE algorithms maintain universal computational capability with continuous resource scaling. Since these represent incompatible mathematical structures, P ≠ PSPACE. Our approach models P as time-constrained computation with finite computational scope, and PSPACE as space-constrained computation with unlimited computational scope, revealing the fundamental trade-offs that separate these complexity classes.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.17048774

Authors: raman, chetan, sonnet 4, claude

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7079627838

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