Some Decision Problems Concerning Semilinearity and Commutation

Harju, Tero; Ibarra, Óscar H.; Karhumäki, Juhani; Salomaa, Arto

doi:10.1006/jcss.2002.1836

Cited by 58 publications

(42 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The k-valuedness problem is therefore reduced to the emptiness problem for those counter machines. We prove that the procedure of [HIKS02] to decide this emptiness problem can be executed in coNPTime and as a consequence, the k-valuedness problem for VPT is decidable in co-NPTime.…”

Section: Outline Of the Documentmentioning

confidence: 96%

“…First we show that the procedure in [HIKS02] for deciding emptiness of such machines can be executed in co-NPTime. Second, as a direct consequence, we show that the procedure for deciding the multiple morphism equivalence problem in [HIKS02] can be executed in co-NPTime. Finally, we show how to use this last result to decide the k-valuedness problem for VPTs in co-NPTime.…”

Section: K-valued Vptsmentioning

confidence: 99%

“…Following [HIKS02], one extends the alphabet Σ with 3k letters + j , − j , s j ∈ Σ intended to simulate the increasing, decreasing transitions of the j-th counter, and the transitions that do not change the j-th counter (skip). We denote by Σ + this alphabet.…”

Section: )mentioning

confidence: 99%

“…The multiple morphism equivalence problem was proved to be decidable in [HIKS02] on any class of languages whose Parikh images are effectively semilinear. In the case of context-free languages, we show that it can be decided in co-NPTime.…”

Section: Multiple Morphism Equivalence Problemmentioning

confidence: 99%

“…In order to prove this theorem, we briefly recall the procedure of [HIKS02] in the particular case of pushdown machines. In order to decide the morphism equivalence problem of ℓ pairs of morphisms on a CFL L, the idea is to construct an RBCPA(1, 2ℓ) that accepts the language…”

Section: Multiple Morphism Equivalence Problemmentioning

confidence: 99%

See 4 more Smart Citations

Visibly Pushdown Transducers

Raskin

Servais

2008

Automata, Languages and Programming

View full text Add to dashboard Cite

Section: Outline Of the Documentmentioning

confidence: 96%

Section: K-valued Vptsmentioning

confidence: 99%

Section: )mentioning

confidence: 99%

Section: Multiple Morphism Equivalence Problemmentioning

confidence: 99%

Section: Multiple Morphism Equivalence Problemmentioning

confidence: 99%

See 3 more Smart Citations

Visibly Pushdown Transducers

Raskin

Servais

2008

Automata, Languages and Programming

View full text Add to dashboard Cite

A Matrix Q-Analogue of the Parikh Map

Eğecioǧlu

Ibarra

IFIP International Federation for Information Processing

View full text Add to dashboard Cite

We introduce an extension of the Parikh mapping called the Parikh mapping, which takes its values in matrices with polynomial entries. The morphism constructed represents a word over a alphabet as a upper-triangular matrix with entries that are nonnegative integral polynomials in variableWe show that by appropriately embedding the alphabet into the alphabet and putting we obtain the extension of the Parikh mapping to (numerical) matrices introduced by Mateescu, Salomaa, Salomaa, and Yu. The Parikh mapping however, produces matrices that carry more information about than the numerical Parikh matrix. The entries of the image of under this morphism is constructed by the number of occurrences of certain words as scattered subwords of

show abstract

Characterizations of Some Restricted Spiking Neural P Systems

Ibarra

Woodworth

2006

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. A k-output spiking neural P system (SNP) with output neurons, O1, ..., O k , generates a tuple (n1, ..., n k ) of positive integers if, starting from the initial configuration, there is a sequence of steps such that during the computation, each Oi generates exactly two spikes a a (the times the pair a a are generated may be different for different output neurons) and the time interval between the first a and the second a is ni. After the output neurons have generated their pairs of spikes, the system eventually halts. Another model, called k-train SNP, has only one output neuron. It generates a k-tuple (n1, ..., n k ) if, starting from the initial configuration, the output neuron O generates the spike train aa...a with exactly k + 1 a's such that the interval between the i th a and the i + 1 st a is ni, and the system eventually halts. We assume, without loss of generality, that each neuron in the SNP is either bounded or unbounded. (Bounded here means that there is a fixed constant c such that at any time during the computation, the number of spikes in the neuron is at most c. Otherwise, the neuron is unbounded.) It is known that 1-output SNPs (= 1-train SNPs) are universal, i.e., they generate exactly the recursively enumerable sets over N . Here, we show the following:1. For k ≥ 1, a set Q ⊆ N k is semilinear if and only if it can be generated by a k-output SNP, where every unbounded neuron satisfies the property that once it starts "spiking" it will no longer receive future spikes (but can continue spiking). This result also holds for k-train SNP. 2. The set Q = {(m, 2m) | m ≥ 1} (which is semilinear) cannot be generated by any 2-output bounded SNP (i.e., SNP all of whose neurons are bounded). Thus, for k ≥ 2, there are semilinear sets over N k that cannot be generated by k-output bounded SNPs. This contrasts a known result that 1-output bounded SNPs generate all semilinear sets over N . 3. For k ≥ 2, k-output bounded SNPs are computationally more powerful than k-train bounded SNPs. (They are identical when k = 1.) 4. For k ≥ 1, k-output bounded SNPs and k-train bounded SNPs can be characterized by certain classes of nondeterministic finite automata with monotonic counters.

show abstract

Some Decision Problems Concerning Semilinearity and Commutation

Cited by 58 publications

References 14 publications

Visibly Pushdown Transducers

Visibly Pushdown Transducers

A Matrix Q-Analogue of the Parikh Map

Characterizations of Some Restricted Spiking Neural P Systems

Contact Info

Product

Resources

About