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Questions tagged [linear-bounded-automata]

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Defining the halting problem for non-deterministic automata

The primary definition of Turing machine (TM), at least in my own reference textbook (Hopcroft+Ullman 1979) is deterministic. Hence my own understanding of the halting problem is primarily for deterministic TM, though I am aware that it may be…
babou
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Why is the halting problem decidable for LBA?

I have read in Wikipedia and some other texts that The halting problem is [...] decidable for linear bounded automata (LBAs) [and] deterministic machines with finite memory. But earlier it is written that the halting problem is an undecidable…
user5507
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Why are Linearly Bounded Turing Machines more powerful than Finite State Automata?

I was under the impression that our computers, being finite, are ultimately no more powerful than (extraordinarily large) Finite State Machines. However, Linearly Bounded Turing Machines are also finite, but it seems that Regular Languages are…
Ben I.
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Is a LBA with stack more powerful than a LBA without?

Even so a linear bounded automata (LBA) is strictly more powerful than a pushdown automata (PDA), adding a stack to a LBA might make it more powerful. A LBA with stack should not be Turing complete, because its halting problem should be decidable.…
Thomas Klimpel
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A push-down automaton with two stacks which is equivalent to a linear-bounded automaton

It is known that a PDA with two stacks is equivalent to a TM. On the other hand a PDA with one stack is capable to recognise only context-free languages. Hence there is a kind of a gap between the class of PDA with one stack and the class of PDA…
Andrey Lebedev
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Time complexity of languages recognized by linear bounded automata with restricted number of writes

Suppose that $L$ is a language recognized by a linear-bounded automaton with the constraint that it can only change each of its input cells at most $t$ times each, where $t$ is some constant integer. Must $L$ belong to $P$, the class of languages…
L.Yi
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Is $E_{LBA}$ a Turing-recognizable language?

I know that $E_{LBA} = \{\langle M \rangle ~ \mid ~ L(M) = \emptyset \}$ is an undecidable language, but is it recognizable (recursively enumerable)? It seems that it's complement is recognizable since we could construct a Turing machine that…
Richard
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Is every language in PTime also context-sensitive?

Context-sensitive languages are exactly those that can be recognised using linearly bounded automata, i.e., those in NSPACE(O($n$)). This subsumes all languages that can be recognised in linear time, i.e., DTIME(O($n$)), since you can only use n…
mak
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Is it possible to convert LBA into DFA?

Today I learned about an abstract class of machines called linear bounded automata. It is intended to model real-world computers that have a limited amount of memory. I have always thought that real computers are DFAs due to the finite memory (but…
juhist
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Algorithms to match regular expressions containing backreferences

I'm trying to come up with an implementation of a matcher for regular expressions containing backreferences like: ([a-c])x\1 which would match axa, bxb and cxc but nothing else. While I've seen a number of posts about the theory about what is the…
Radu Stoenescu
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Restrictions to counter machines capturing LBA

As you know in computation theory, there is a simple programming language equivalent in power to Turing machines. It is described as follows: Values: natural numbers only, but of unlimited precision. • Variables: – Input variables X1, X2, X3, . . .…
NedaHn
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Is there a grammar type for deterministic LBA?

Contextsensitive grammars define exactly the langauges acceptable by nondeterministic LBA. But how about deterministic LBA - is there a grammar type capturing exactly the languages acceptable by this restricted automaton type? (Just as contextfree…
lukas.coenig
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Find a linear bounded automaton that accepts the language $L = \{ a^{n!} : n \geq 0 \}$

I need to construct linear bounded automaton for the language $L = \{ a^{n!} : n \geq 0 \}$. I know how LBA functions, however, I don't have a thought how it can check the n! that to in the power of a. I might want to hear a few suggestions, as I am…
Ajinkya Taranekar
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Recognizing loops in computation on LBA

In the case of LBAs (Linear Bounded Automaton), in writing a decider for the language $\qquad A = \{ \langle M,w\rangle \mid M\ \mathrm{LBA}, w \in \mathcal{L}(M) \}$ we reject the input after a specific number (number of possible different…
Mahdi
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Prove that it is undecidable whether a given LBA accepts a regular set

I know for an LBA the emptiness problem is undecidable. However I am not clear on how to reduce the halting problem of Turing machines to this as LBAs are strictly computationally less powerful than Turing machines. Or should I approach with…
Arka Pal
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