Problem Detail: I am trying to (intuitively) understand the two terms “decidability” and “verifiability”. I have done a reasonable amount of searching and going through the various texts I can put my hands on. However, their intuitive understanding seems to escape Read More …
Author: ignougroup
[Solved]: Is this variant of ATM decidable?
Problem Detail: Ok so I understand how $mathrm{ATM} = {langle M,w rangle mid text{$M$ is a TM and $M$ accepts $w$}}$ is undecidable. Is this because $w$ is a variable? What if the parameter is fixed? Consider $mathrm{BTM} = {langle M,w Read More …
[Solved]: Calculating cache memory based on LRU algorithm
Problem Detail: Assuming i have 4 blocks of cache memory, Using the LRU (Least Recently Used) replacement algorithm on this following sequence of access to memory blocks: 1 2 3 4 5 2 5 4 1 5 2 3 : 1 Read More …
[Solved]: Are regular languages closed under sort (Parikh image)?
Problem Detail: Assume $L$ is a regular language over an ordered alphabet. Is the language built by taking every word in $L$ and sorting it always a regular language? Asked By : Andrew MacFie Answered By : Niel de Beaudrap No. Counterexample: assuming Read More …
[Solved]: Direct Cache Mapping – Determine Tag Size
Problem Detail: In the following direct cache map, there is a list of 32-bit memory address references, given as word addresses. I gathered that the index size is 3 bit and there is no offset. However, I used 4 bits to Read More …
[Solved]: Algorithm for type conversion / signature matching
Problem Detail: I’m working on an expression typing system and looking for insights on what algorithms may be available which solve my problem — or a proof that its complexity is too high to be reasonable to implement. The problem is Read More …
[Solved]: Why do reductions to NP-complete problems in NTIME(n) not break the nondeterministic time hierarchy?
Problem Detail: Let $mathrm{L} in mathrm{NTIME}(n^3)$. Since $mathrm{NTIME}(n^3) subseteq mathrm{NP}$, we have that $mathrm{L} le_p mathrm{3SAT}$. However, $mathrm{3SAT} in mathrm{NTIME}(n)$. Hence, $mathrm{L} in mathrm{NTIME}(n)$. Thus, $mathrm{NTIME}(n^3)subseteq mathrm{NTIME}(n)$ which implies the non-deterministic time-hierarchy is false. But we all know that time hierarchy Read More …
[Solved]: Variable Length Encoding of Integers
Problem Detail: I was just researching Fibonacci encoding of integers. Numbers are encoded in binary and where no two consecutive bits are equal to 1 – other than to terminate the number. Now other schemes are possible, for example having three Read More …
[Solved]: Can we move quantifiers to the left in predicate logic?
Problem Detail: Say I have part of a query in the form: ∃xa(…)∧∃xb(…)∧∃xc(…), where a, b, and c are attributes and the ellipses can be anything (I’m looking for a general rule). Is this equivalent to saying ∃xa,xb,xc(…∧…∧…) – i.e. compacting Read More …
[Solved]: Time cost of thread creation
Problem Detail: While creating an algorithm, the following question came up: In uniform cost, what is the time cost of a process that creates a thread? Is there a difference between creating a thread in a thread pool vs creating a Read More …
