Insertion operations on deterministic reversal-bounded counter machines

Eremondi, Joseph; Ibarra, Óscar H.; McQuillan, Ian

doi:10.1016/j.jcss.2018.02.003

Cited by 5 publications

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“…Let NPCM be the set of machines with one pushdown, and some number k of counters where the pushdown is unrestricted, but the counters are reversal-bounded. The family of languages accepted by NPCM [1,25] is of interest since it has a decidable emptiness and membership problem, and only accepts semilinear languages.…”

Section: Definitionmentioning

confidence: 99%

On store languages of language acceptors

Ibarra

McQuillan

2018

Theoretical Computer Science

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It is well known that the "store language" of every pushdown automaton -the set of store configurations (state and stack contents) that can appear as an intermediate step in accepting computations -is a regular language. Here many models of language acceptors with various store structures are examined, along with a study of their store languages. For each model, an attempt is made to find the simplest model that accepts their store languages. Some connections between store languages of one-way and two-way machines are demonstrated, as with connections between nondeterministic and deterministic machines. A nice application of these store language results is also presented, showing a general technique for proving families accepted by many deterministic models are closed under right quotient with regular languages, resolving some open questions (and significantly simplifying proofs for others that are known) in the literature. Lower bounds on the space complexity of Turing machines for having non-regular store languages are obtained.Hence, the following is immediate:Corollary 41. There is a middle log log n space-bounded 2DTM M such that S(M ) is not regular. Turning now to one-way machines:Proposition 42. If M is a middle s(n) space-bounded 1NTM and s(n) grows slower than log n, then S(M ) is regular.Proof. The proof is the same as the proof of Proposition 38 using Proposition 37, part 2, and noting that the M ′ constructed in that proof would also be one-way if M is one-way.Corollary 43. If M is a strongly s(n) space-bounded 1NTM and s(n) grows slower than log n, then S s (M ) is regular.

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Section: Definitionmentioning

confidence: 99%