An escalation in required computational resources (time, memory, intermediate space) caused by syntactic features, encodings, algorithmic choices, or specific problem instances that make computation impractical.

Principle

Certain encodings or transformations can enlarge representation size or intermediate structures (for example, duplicating subexpressions or expanding quantifiers), and algorithmic processes may have worst-case resource usage that grows superpolynomially with input size.

Demonstration

Converting a formula to disjunctive normal form (DNF) can blow up exponentially in length; eager expansion of definitions or naive grounding of quantified formulas in a large domain may exhaust memory and time even when the original specification is compact.

Misapplication

Choosing encodings or algorithms that implicitly materialize exponentially many intermediate results (for example, fully expanding combinatorial constructions) under the assumption that problem size remains small, leading to system crashes or unbounded runtimes.

Consequence

Awareness of resource blowup leads to alternative encodings, lazy evaluation, symbolic representations, streaming, or approximation; when addressed correctly, it restores feasibility and predictable resource bounds for intended use cases.

Reversal

Resource containment — algorithmic and representational choices that keep time and space within acceptable bounds (e.g., polynomial-time encodings, streaming algorithms, incremental methods).

Boundary

Refers to resource costs arising from representations, encodings, or algorithmic expansions; distinct from mere algorithmic complexity classification (e.g., P vs NP) insofar as blowup often stems from particular encodings or preprocessing choices rather than inherent decision complexity.

Semantic Tension

Closely related to search-space explosion: one describes combinatorial candidate growth, the other emphasizes actual measured resources consumed; mitigation techniques overlap but may prioritize memory layout, streaming, and incremental evaluation over search heuristics.

Synthesis

Resource blowup is the practical failure mode where representations or algorithmic steps create prohibitively large time or memory demands; resolving it requires choosing encodings and evaluation strategies that avoid materializing large intermediate structures and exploit laziness, modularity, or approximation.