Icalp writing style

ICALP Writing Style

Build the ICALP skeleton: model → theorem → improvement → technique → complete proof. ICALP referees are subject experts who will check the mathematics, so the writing has two jobs at once — make the contribution legible on the first page, and make the proofs verifiable in the body, appendix, and full version. The 15-page body is a hard budget; exposition, not omission, is how you fit.

The first-page arc

1. State the model, then the theorem. Fix the exact setting — the computational model, the complexity measure, the class of objects — before the claim. "Fully dynamic, deterministic, worst-case update time" comes before "n^{o(1)}."
2. Put a legible theorem statement in the abstract. A specialist should read the abstract and know what you proved and by how much, without opening the proof.
3. Position against a named prior bound. State the best previous result and your improvement in the same breath. "The best known bound was X; we give Y" is the ICALP sentence.
4. Name the barrier and the technique. Say what obstruction prior work hit and what idea gets past it. Referees reward a clearly identified new technique over an opaque win.
5. Say where the proof lives. The body may sketch; point explicitly to the appendix / full version where each claim is proved in full.

Track-aware voice

• Track A (Algorithms, Complexity, Games): lead with the bound. The reader wants the running time / approximation ratio / complexity class and the comparison to prior work up front; the technique section then shows how.
• Track B (Automata, Logic, Semantics): lead with the model and the exact question — the fragment of logic, the class of automata, the calculus — and the decidability/complexity/ characterization you establish. Definitional precision is itself part of the contribution.

The 15-page discipline

• The body sketches proofs and proves the key lemmas; routine or long proofs go to the labelled appendix / full version. But the body must contain enough that a referee can follow the argument and locate every deferred step (icalp-supplementary).
• Recover space by compression, not omission: fold repetitive case analysis, state a general lemma once, cite standard tools rather than re-deriving them. Do not shrink margins or fonts — the LIPIcs style is fixed.
• A body padded to 15 pages with all proofs banished to an unread appendix is a scored risk: reviewers judge on the body and distrust a paper whose substance they cannot see.

Theorems, definitions, and the proof contract

• Every headline theorem has a complete proof the referee can find — in the appendix if not the body. "Details omitted" with no full version is the classic ICALP soundness failure.
• Definitions before use, notation minimal. Introduce only the notation the proof needs; a wall of symbols on page 2 loses the reader before the theorem.
• State lemmas so the proof structure is visible. A reader should be able to reconstruct the dependency graph of lemmas from their statements.

Upper and lower bounds together

ICALP prizes tightness. When you can, pair an algorithm with a matching (possibly conditional) lower bound, or a decidability result with a complexity classification. A result that is provably optimal in its parameter reads far stronger than an isolated upper bound — and it pre-empts the referee's "is this tight?" question.

Anti-patterns (theory-specific)

• Benchmark framing. "Fast on these instances" is experimental-algorithms voice; ICALP wants a provable bound (an icalp-topic-selection re-route signal if there is no theorem behind it).
• Buried theorem. A first page about how "important and active" the area is, with the actual statement on page 6.
• Unpositioned improvement. A bound with no comparison to the best known result — the referee cannot tell if it is progress.
• Proof-by-intimidation. Dense symbol-pushing that hides a gap; referees who cannot check a step treat it as unproved.
• Over-signposted roadmap substituting for a statement of the result.

Self-check before drafting the body

[Model] is the computational model / logical fragment fixed before the first theorem?
[Legibility] can a specialist state my result and its improvement from the abstract alone?
[Positioning] is the best prior bound named and my delta stated against it?
[Barrier] is the obstruction prior work hit, and my technique for evading it, identified?
[Proof contract] does every headline theorem have a complete proof the referee can find?
[Tightness] is there a matching lower bound / optimality statement where one is expected?

Output format

[Track] A / B — and the corresponding lead (bound vs model+question)
[First-page arc] model -> theorem -> improvement -> technique -> proof-location: all present? gaps?
[Page budget] body <=15pp excl. refs+appendix; compression targets
[Proof contract] theorems lacking a complete proof somewhere: <list>
[Tightness] matching lower bound present / justified absent
[Rewrite queue] <ordered edits to reach the ICALP bar>