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By Javier Esparza, Pierre Fraigniaud, Thore Husfeldt, Elias Koutsoupias

This two-volume set of LNCS 8572 and LNCS 8573 constitutes the refereed complaints of the forty first overseas Colloquium on Automata, Languages and Programming, ICALP 2014, held in Copenhagen, Denmark, in July 2014. the full of 136 revised complete papers awarded including four invited talks have been conscientiously reviewed and chosen from 484 submissions. The papers are prepared in 3 tracks focussing on Algorithms, Complexity, and video games, good judgment, Semantics, Automata, and thought of Programming, Foundations of Networked Computation.

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Extra info for Automata, Languages, and Programming: 41st International Colloquium, ICALP 2014, Copenhagen, Denmark, July 8-11, 2014, Proceedings, Part II

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Bell et al. Let the truth values of propositions be 1 (true) and 0 (false). Let ◦ : {0, 1} × ∗ {0, 1} → {0, 1} be a binary boolean function. Extend ◦ to a function ◦ : 2Σ × ∗ ∗ 2Σ → 2Σ : If w ∈ Σ ∗ and L, L≥ ⊆ Σ ∗ , then w ∈ (L ◦ L≥ ) ⇔ (w ∈ L) ◦ (w ∈ L≥ ). Also, extend ◦ to a function ◦ : 2Qm × 2Qn → 2Qm ×Qn : If q ∈ Qm , q ≥ ∈ Qn , F ⊆ Qm , and F ≥ ⊆ Qn , then (q, q ≥ ) ∈ (F ◦ F ≥ ) ⇔ (q ∈ F ) ◦ (q ≥ ∈ F ≥ ). Suppose that A = (Q, Σ, δ, 0) and A≥ = (Q≥ , Σ, δ ≥ , 0) with |Q| = m and ≥ |Q | = n are uniformly minimal DFSs, and ◦ is any proper boolean function.

The problem of determining the complexity of an operation [1,8,15,16] on regular languages has received much attention. It is defined as the maximal complexity of the language resulting from the operation, taken as a function of the complexities of the operands. When operations are performed on large automata it is important to have some information about the size of the result and the time it will take to compute it. The quotient complexity of an operation gives an upper bound on its time and space complexity [15].

For example, in the class of regular right ideals – languages L ⊆ Σ ∗ satisfying L = LΣ ∗ – languages K and K ≥ are appropriate, but L and L≥ are not. The main result of the present paper has been applied to right ideals in [4], where the proof that the witnesses used there meet the bounds for boolean operations was greatly simplified with the aid of our theorem. 3. When one studies combined operations – operations that involve more than one basic operation, for example, the intersection of reversed languages – one again need new witnesses [7].

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