Questions tagged [computation-models]

The definition of the set of allowable operations used for computation and their respective costs. Some examples of models include Turing machines, recursive functions, lambda calculus, and production systems.

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Machines for context-free languages which gain no extra power from nondeterminism

When considering machine models of computation, the Chomsky hierarchy is normally characterised by (in order), finite automata, push-down automata, linear bound automata and Turing Machines. For the ...
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Turing Machine-Like Formalism for The Actor Model

Turing machines have a formal symbol alphabet, state and transition-rules based description of how a computation is done. The Actor Model is sometimes mentioned as a more powerful computational-...
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Automata that is Turing complete if you add a nondeterminism

Pushdown automata have an interesting property: non-deterministic ones belong to a different computational class than deterministic ones. This is in contrast to finite state and turing machines, for ...
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Make a tag system simulate a finite automaton?

Tag systems are Turing-complete. I was wondering if there is any easy way to create tag systems that simulate finite automata. So create tag systems that recognize languages, e.g. by having at the end ...
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Automaton equivalent of the π calculus?

If Turing Machines are the automata equivalent of the $\lambda$ calculus, what is the automaton equivalent of the $\pi$ calculus? I suppose it would be some class of automata that resembled a Turing ...
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What is the difference between quantum computing and parallel computing?

Quantum computing essentially relies on the fact that qubits maintain multiple possible states simultaneously. Parallel computing too processes multiple states simultaneously. So what is the ...
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Computational power of Actor Model

In the question below, let TM be Turing machine, NTM be nondeterministic Turing machine and PTM be probabilistic Turing machine. In his paper "Actor Model of Computation: Scalable Robust Information ...
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Model Join calculus as hypergraphs

I'm not sure if this is the right site to ask, but I couldn't find a another one. Some time ago I found out about the join calculus. It is based on constructs called joins to support concurrency. For ...
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The cost of memory allocation on the (tacitly assumed) Word RAM machine?

Consider a particular algorithm that solves the binary search problem (or similar stuff) by performing $\sqrt{n}$ simple operations on numbers of $\log(n)$ bits. Suppose this algorithm works on a <...
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Real RAMs with “reasonable” operations

There is a large body of literature on RAMs with "reasonable" and "unreasonable" operations, where "unreasonable" operations would yield a machine with too much power to be practically feasible. For ...
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125 views

Is a reduced Wang B-machine Turing-complete?

A Wang B-machine has only 4 instructions: right: Move tape head right left: Move tape head left ...
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63 views

What is the role of abstract machines in the Curry-Howard isomorphism?

By abstract machines I mean things like the SECD machine, Krivine's machine or more generally machines with states/memory/registers/stack/accumulator... According to Wikipedia page of the Curry-...
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Computational complexity of emulating (untyped) λ-calculus with a queue machine

I am looking for bounds - both lower and upper - on the time, spacial, and state/symbol (i.e. number of states and symbols required) complexity of simulating the (untyped) λ-calculus with a queue ...
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1answer
737 views

How to simulate a bidirectional TM on a regular one with time factor four?

In Computational Complexity A Modern Approach, one claim says that if $f$ is computable in time $T(n)$ by a bidirectional TM $M$, then it is computable in time $4T(n)$ by a unidirectional TM $\tilde{M}...
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Advances in recent time in Von-neumann self replication idea

I have read about Von-neumann self replication from Theory of Self-reproducing automata, which are lecture notes reconstructed from lectures in book of the same name. Theory of Self-reproducing ...
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Alternative to a CALL as a composition?

I've seen a numerous interesting abstract machines (i.e. CESK) and evaluators (diverse meta-circular S-expression evaluators, i.e. vau, COLA) and other models (concatenative, SK/Lambda calculus) which ...
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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. ...
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Can we define CFL without grammars or automata?

The set of regular languages $R$ over an alphabet $\Sigma$ can be defined as the smallest set satisfying these 5 axioms: Empty language: $\{\} \in R$ Singleton languages: $\forall a \in \Sigma : \{a\}...
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Why does using an encoding trick like Gödel numbers make a register machine universal?

Here the author describes the Random Access Stored Program machine and the problem of indirect addressing. The author states: But this does not solve the problem (unless one resorts to Gödel ...
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How does one program in a tag system?

I've played with 2-tag systems a bit and read all about tag/lag systems. They're great for experimenting with computation, and obviously useful as intermediaries in various proofs. My question is: ...
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Similarities between Babbage's difference engine and the Turing machine

What would you consider similarities between the difference engine and the Turing machine? At this point I feel I know how they both function, yet I can't point out any worthwhile similarities between ...
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Equivalence between different Turing Machines and a definition of simulation

Im having some difficulty understanding how the following two concepts could be related. Equivalence between TMs as is commonly tought According to this site answer, to prove a standard TM model to ...
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Is the language $L$ of coded CFG's Turing decidable?

Consider the following language $L$ = {$<G><w>$ | $G$ is a CFG and $w\in L(G)$} Now, I wish to prove that $L$ is Turing decidable. My gut tells me to construct a Turing machine that ...
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What is the relationship between “model of computation” and “algorithm”?

Traditionally, the usual definition you find for model of computation is "an abstract description of how an output is computed given an input" (Wikipedia and my TCS course are my sources, but the ...
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Simulating QC using nondeterministic Turing machine

Is it more efficient to simulate Quantum Computer using a non-deterministic Turing machine? Would it be more efficient than simulation using a deterministic Turing machine or probabilistic Turing ...
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Is the set of admissible numberings recursively enumerable?

For each admissible numbering, pick at least one pair of programs (but not necessarily all, which is impossible anyway) where the first translates from a given admissible numbering to that one, and ...
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Explaining TM notation in Lewis/Papadimitriou

I was working on some questions in the book "Elements Of The Theory Of Computation", by Lewis and Papadimitriou, and I need help with one question - question 4.1.8 (chapter 4): Give the full ...
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Typed representation of a memory model

Assume a simple procedural language, where statements write and read from local memory via references and procedures accept arguments of n different scalar types (say floats, ints and strings) and ...
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ORAM: Is it generic?

Recently, plenty of researchers are looking at designing efficient data-oblivious algorithms. Roughly speaking, an algorithm is said to be data-oblivious if its data access patterns are independent of ...
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A linear code, what is that?

I have been trying to understand the polytope model used for loop nest optimizations. Now while going through some of the thesis written on this, i came across the term/phrase "linear code" a number ...
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Expressing classic automata in modern terms

This semester I was introduced to finite automata (FSM), then pushdown automata (PDA), and now the Turing machine (TM). Granted that there're many possible implementations of these abstractions (...
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NPDA, guessing capability and stack as an exclusive resource

Context Free languages is exactly the class of languages recognized by Nondeterministic Push Down Automata (NPDA). We can view a nondeterministic transition as a guess; for example if $L = \{x x^R \}$...
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583 views

λ-Calculus extensions: meaning of extension symbols

When working with λ-Calculus I see lots of extensions that use other symbols such as ∀ <:Top {} ←, which are from "Types and Programming Languages" (WorldCat) by Benjamin C. Pierce. ...
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Can differennt computation model lead to different complexity?

There are many examples where someone replaces a CPU with a GPU or an FPGA and get a performance boost of $\times 100$ or more, but is it possible for a change in the architecture of computational ...
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Complexity classes for various models of computation

The various complexity classes usually taught and studied ($P$, $NP$ $co-NP$, EXP, NSPACE etc) are usually defined using Turing Machines as the preferred model of computation. Are these sets of ...
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Theory for programs that are “embedded” in other programs?

We can make the following distinctions: (I will use the term "program" and "machine" as synonyms). A (baseline) machine. This can be formalized by a Turing machine. It receives an input, and computes ...
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General notion of memory for a computational model

I have just started studying Michael Sipser's Theory of Computation, studying various computational models such as FAs, PDAs et cetera. In the book, the term "memory" was often used,as in the case of ...
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RO turing machine with finite memory

Consider the following: A weak TM is a TM with finite tape in size $k$ which can only read its input values. note: the tape size does not include the input length. I need to determine whether if the ...
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Alternatives to Sequential Computation

When software boils down to assembly, it is just a sequence of instructions like this: ...
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103 views

Doubt on dovetailing

Let < M > be an encoding of a Turing machine. L = { < M > | M is a Turing machine that accepts a string of length 2014 } Above language is R.E(even though we have infinite TM's) as we have ...
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Formal definition of simulation

Assume that the model of computation is a standard Turing machine model with input alphabet $\Sigma = \{0,1\}$, work alphabet $\Gamma = \{0,1,\_\}$, 1 input tape, 1 work tape and 1 output tape. We ...
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Addition Register Machine

In an abstract register machine, is it possible to add two registers together without losing one of the summands, but without using a third register? That is to have a register machine that maps $(m,...
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Generate a graph to exact size using Kronecker product graph model

In network science, we can take sample a complex system and derive from this sampling a representative network (or graph) that describes the system to some extent. A model of a network, is a powerful ...
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Construct DFA given oracle access to the language

I was given the following question. Given a minimal DFA $A$ with $m$ states over some alphabet $\Sigma$ which is a "black box" (you can only run words to it and it tells you if it accepts or not): ...
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About the SOS degree of a function and optimization algorithms for the function

Given a non-negative function on the hypercube $f : \{0,1\}^n \rightarrow \mathbb{R}_{\geq 0}$ one says that it is of "SOS-degree" of $d$ (denoted as $deg_{SOS}(f) =d$) if $d$ is the minimum $k$ such ...
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Markov algorithm: pick rule first, then position, or the other way around?

A Markov algorithm is a string rewriting system (well, not a set of rules but a list of rules since they need to be ordered) with a strategy for applying rules that ensures determinism. I think the ...
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311 views

Reducing states in a finite-state machine using compatibility classes, for an incompletely specified machine

In the process of reducing the states of a synchronous finite state machine first we need to create maximal compatibility classes (of states; which states can be compatible, i.e. the "don't cares" can ...
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How to model most optimized encoding of string data

Sorry if this question isn't super well defined, I am just struggling currently with figuring out what an "ideal solution" looks like to the following problem, and haven't pinned down an equation. I ...
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Formal definiton of RAM model with D disks of blocks B, fast memory M and P processors

In some articles I've read of RAM model with D disks of blocks B, fast memory M and P processors. Is there a formal deifition of that model?
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What is difference between a formal system and a model of computation

I don't exactly know the difference--partly because I cannot find a mathematical definition for a model of computation (also why is this)?