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Questions tagged [pspace]

The tag has no usage guidance.

-2
votes
1answer
119 views

Why $PSPACE!=Dtime(2^n)$? [closed]

Why $PSPACE != Dtime(2^n)$? I can not see how padding argument can help here, how can it be proven?
-2
votes
1answer
240 views

Why is it a mystery if PSPACE ?= EXPTIME?

It seems obvious to me that $PSPACE \neq EXPTIME$. I, however, do not believe that my seemingly obvious logic would not be picked up by more intelligent people if it was so simple, so I'm assuming ...
3
votes
0answers
182 views

Implications of resolving $BPP$ vs $PSPACE$

The relationship between the complexity classes $BPP$, $P$, and $NEXP$ is currently undetermined. We know that $P \neq EXP$ by the time hierarchy theorem, but we don't know if $BPP = P$ (as many ...
8
votes
0answers
130 views

Practical interactive proof schemes for NP-hard problems

Model-checking (in the sense of reachability in a succinct graph) is PSPACE-complete. SAT is NP-complete. Both problems are considered intractable, yet there exist tools capable of solving them on ...
0
votes
1answer
184 views

How to prove $P^{Halt} = PSPACE^{Halt}$ [closed]

Halt means the halting set. $PSPACE^{Halt}$ is the class of problems that can be solved with polynomial memory (possibly exponential time), given a halting oracle.
16
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0answers
270 views

Intermediate problems between PSPACE and EXPTIME

Intermediate problems between P and NP are quite famous, and are sometimes considered as complexity classes by themselves. Do you know of any problem that is known to be PSPACE-hard and in EXPTIME, ...
5
votes
1answer
888 views

Does P = NP imply NP being a strict subset of PSPACE? [closed]

Does $\textbf{P} = \textbf {NP}$ imply that $\textbf{NP} \subsetneq \textbf{PSPACE}$? Or, for a slightly stronger result, does it imply that $\textbf{NL} = \textbf P$?
8
votes
1answer
236 views

Does there exist an oracle $A$ such that $(P^{\#P})^{A} \neq PSPACE^{A}$?

Background We know that $P^{\#P} \subseteq PSPACE$. In addition, we known from Toda's theorem that $PH \subseteq P^{\#P}$. For more background on $\#P$, see here: https://en.wikipedia....
17
votes
1answer
418 views

What is the minimum complexity oracle that separates PSPACE from the polynomial hierarchy?

Background It is known that there exists an oracle $A$ such that, $PSPACE^A \neq PH^A$. It is even known that the separation holds relative to a random oracle. Informally, one may interpret ...
4
votes
0answers
138 views

More powerful generator than Nisan-Wigderson one

Nisan-Wigderson generator can be computed in $\log^{O(1)} n$ space and fools all constant-depth circuits of size poly($n$). I mean Theorem 5 here. I want another generator, that can be computed in ...
10
votes
0answers
151 views

Checking a long product of matrices

Given a set of n-by-n integer matrices $\{A_1, \dots, A_m\}$, for a word $w=w_1 w_2\cdots w_l$ over $\{1, \dots, m\}$, we define $A_w:=A_{w_1}\cdots A_{w_l}$. The question is to decide, given $\{A_1,...
8
votes
1answer
224 views

Consequences of a distillation algorithm for PSPACE

The following notion of a distillation algorithm comes from "On Problems Without Polynomial Kernels". Let a language $L$ be given. A distillation algorithm for $L$ takes a given list of input ...
5
votes
0answers
193 views

Easy interactive proofs for easy problems?

Motivation Consider some $L \subseteq \{0,1\}^*$. Suppose Alice gives Bob a machine or oracle $M$ that purportedly decides $L$. If Bob has only polynomial time in their disposal, then they cannot ...
1
vote
0answers
51 views

Circuit games in extensive form with imperfect information

Consider $l,m,n,N \in \mathbb{N}$ and circuits $C: \{0,1\}^{l+m} \rightarrow \{0,1\}^l$, $D: \{0,1\}^{l+n} \rightarrow \{0,1\}^l$. Consider the following zero-sum two-layer extensive-form game with ...
21
votes
1answer
352 views

For which regular expressions $\alpha$ is $\{ \beta \mid L(\alpha) = L(\beta) \}$ PSPACE-complete?

It is well known that the following problem is PSPACE-complete: Given regular expression $\beta$, does $L(\beta) = \Sigma^*$? What about determining equivalence to other (fixed) regular ...
2
votes
1answer
193 views

Space requirements for solving True Quantified Boolean Formulas problem [closed]

I came across this section on the wikipedia page for the TQBF solving problem, and just can't wrap my head about the fact that the space requirement is linear. Moreover, it does not provide any ...
2
votes
0answers
120 views

Space time lower bound with $\mathsf{PSPACE}$ oracle

Does a single tape Turing machine with access to $\mathsf{PSPACE}$ oracle needs more than $\mathsf O(1)$ working tape memory and $\mathsf O(1)$ working time to solve $\mathsf{NP}$-complete problem? ...
3
votes
1answer
1k views

How can one ACTUALLY minimize a regular expression? [closed]

Minimizing regular expressions (in terms of number of symbols) is PSPACE-complete (for example as discussed here: minimizing size of regular expression). But how do you actually do that (i.e., what ...
24
votes
0answers
702 views

What are consequences of the collapse of CH?

I don't grasp the full complexity of the counting hierarchy $CH$. I understand $CH$ is in $PSPACE$, and contains $PH$ within its second level, due to the Toda's theorem. But, what would be important ...
12
votes
1answer
679 views

Have these coloring games been solved?

In the paper "On the complexity of some coloring games", Bodlaender gives some open questions about the complexity of deciding if player 1 or 2 has a winning strategy in some graph coloring games. ...
11
votes
3answers
304 views

Is there a simple game with asymmetric complexity?

Consider full information two-player combinatorial games that end after a polynomial number of moves, and in an alternating way, the players picks from a finite number of allowed moves. The usual ...
7
votes
1answer
253 views

Is there a gadget that reduces generalized geography to undirected graphs?

The directed Generalized Geography game is well-known to be PSPACE-complete, however, I could not find anything for the undirected version. I saw that in Hans L. Bodlaender, Complexity of path-forming ...
28
votes
3answers
1k views

Is this variation of TQBF still PSPACE-complete?

Deciding if a quantified boolean formula such as $\forall x_1 \exists x_2 \forall x_3\cdots \exists x_n \varphi(x_1, x_2,\ldots , x_n),$ always evaluates to true is a classical PSPACE-complete ...
8
votes
0answers
310 views

Linear space language that requires exponential time without ETH

The $\mathsf{P} \neq \mathsf{PSpace}$ conjecture means that There is a language $L \in \mathsf{DSpace}(O(n^t))$ for some $t>0$ such that for all positive integers $k$, $L$ requires $\Omega(n^k)...
14
votes
1answer
479 views

Does PSPACE-completeness imply approximation hardness?

It is mentioned in a comment in another cstheorySE post that PSPACE-completeness imply APX-hardness. Can anyone please explain/share a reference for it? Is this "tight"? (i.e., are there PSPACE-...
1
vote
0answers
70 views

Different hardness proofs w.r.t different classes

Consider a language $L$ which is hard for some class $C$ (e.g. PSPACE-hard). Trivially, $L$ is also $D$-hard for every class $D\subseteq C$ under the same type of reduction (e.g. NP-hard). Is there a ...
7
votes
1answer
187 views

Coding theory and complete problems

Coding theory is an useful topic in theoretical computer science. There are known examples of problems coming from coding theory which turn out to be NP complete. My questions are the following: $(1)...
12
votes
3answers
311 views

Is there a reduction to “door and pressure plate” games that doesn't explode solution length?

This paper gives a proof that in a game with doors and pressure plates, it is PSPACE-hard to determine whether or not the (player's) avatar can reach a given location. This is proven by a reduction ...
7
votes
0answers
235 views

Is the complexity of ARC KAYLES still open?

In the problem NODE KAYLES two opposing players take turns playing on an undirected graph. In each turn, a player selects a vertex $u$ and removes $u$ and all its neighbors from the graph. The first ...
8
votes
1answer
131 views

Savitch's use of measurability

In Savitch's 1969 paper, "Relationships Between Nondeterministic and Deterministic Tape Complexities", he states that "all common storage functions L(n) >= lg n are measurable. In particular, any ...
2
votes
3answers
969 views

Complexity of Portal 2

I am studying the complexity of Portal 2 and I would like to know if the problem has been studied before. In particular, I would be interested any reference discussing the complexity of Portal 2 and ...
1
vote
2answers
462 views

are there fixed context sensitive grammars which are PSPACE complete?

wikipedia entry says without reference that "There are even some context-sensitive grammars whose fixed grammar recognition problem is PSPACE-complete." This is stronger than saying that CSG is ...
11
votes
1answer
451 views

What is the complexity of counting the number of solutions of a P-Space Complete problem? How about higher complexity classes?

I guess it would be called #P-Space but I have found only one article vaguely mentioning it. How about the counting version of EXP-TIME-Complete, NEXP-Complete as well as EXP-SPACE-Complete problems? ...