On sparse languages L such that LL = Σ

Positive Integers n Such That σ ( φ ( n ) ) = σ ( n )

In this paper, we investigate those positive integers n for which the equality σ(φ(n)) = σ(n) holds, where σ is the sum of the divisors function and φ is the Euler function.

On Parsing LL-Languages

Usually, a parser for an LL(k)-grammar G is a deterministic pushdown transducer which produces a leftmost derivation for a given input string x 2 L(G). Ukkonen 5] has given a family of LL(2)-grammars proving that every parser for these grammars has exponential size. If we add to a parser the possibility to manipulate a constant number of pointers which point to positions within the constructed ...

Angei'iandte Ratlrtrf-\nnr= Tt -l -ll Jttul Ll Ll =

Σ 1 Formulae in Σ L

The essentially Σ1 formulae of ΣL are exactly those which are provably equivalent to a disjunction of conjunctions of 2 and Σ1 formulae.

Very Sparse Leaf Languages

Unger studied the balanced leaf languages defined via poly-logarithmically sparse leaf pattern sets. Unger shows that NP-complete sets are not polynomial-time many-one reducible to such balanced leaf language unless the polynomial hierarchy collapses to Θp2 and that Σ p 2-complete sets are not polynomial-time bounded-truth-table reducible (respectively, polynomial-time Turing reducible) to any ...