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What advantages and disadvantages does Ethereum have over Bitcoin? What can you do with Ethereum that you simply cannot with Bitcoin? What price do you pay for these additional functionalities?

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I'll answer the middle question from the White Paper. Bitcoin can allow simple scripting and a weak version of smart contracts. The scripting that you can do has these limitations (quoting from the white paper, where UTXO means "unspent transaction outputs")

Lack of Turing-completeness - that is to say, while there is a large subset of computation that the Bitcoin scripting language supports, it does not nearly support everything. The main category that is missing is loops. This is done to avoid infinite loops during transaction verification; theoretically it is a surmountable obstacle for script programmers, since any loop can be simulated by simply repeating the underlying code many times with an if statement, but it does lead to scripts that are very space-inefficient. For example, implementing an alternative elliptic curve signature algorithm would likely require 256 repeated multiplication rounds all individually included in the code.

Value-blindness - there is no way for a UTXO script to provide fine-grained control over the amount that can be withdrawn. For example, one powerful use case of an oracle contract would be a hedging contract, where A and B put in $1000 worth of BTC and after 30 days the script sends $1000 worth of BTC to A and the rest to B. This would require an oracle to determine the value of 1 BTC in USD, but even then it is a massive improvement in terms of trust and infrastructure requirement over the fully centralized solutions that are available now. However, because UTXO are all-or-nothing, the only way to achieve this is through the very inefficient hack of having many UTXO of varying denominations (eg. one UTXO of 2k for every k up to 30) and having O pick which UTXO to send to A and which to B.

Lack of state - UTXO can either be spent or unspent; there is no opportunity for multi-stage contracts or scripts which keep any other internal state beyond that. This makes it hard to make multi-stage options contracts, decentralized exchange offers or two-stage cryptographic commitment protocols (necessary for secure computational bounties). It also means that UTXO can only be used to build simple, one-off contracts and not more complex "stateful" contracts such as decentralized organizations, and makes meta-protocols difficult to implement. Binary state combined with value-blindness also mean that another important application, withdrawal limits, is impossible.

Blockchain-blindness - UTXO are blind to blockchain data such as the nonce, the timestamp and previous block hash. This severely limits applications in gambling, and several other categories, by depriving the scripting language of a potentially valuable source of randomness.

Ethereum is designed for contracts and in fact implements a Turing-complete virtual machine on the blockchain.

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    Could you please elaborate on that? What does it mean to be "a Turing-complete virtual machine on the blockchain"? What does "Value Blindness" mean? What does "Blockchain blindness" mean? Where does the state lack (I mean, obviously the system as a whole has the state which bitcoin belongs to whom, doesn't it)? – Martin Thoma Oct 28 '15 at 6:54
  • I've quoted from the white paper. Is there anything still unclear? – paulmorriss Oct 28 '15 at 10:44
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    This is helpful, however I was hoping for a more abstract (hopefully balanced) assessment of the two. This post only answers part of my question and is somewhat biased due to mostly quoting one of the white papers. E.g. it would be interesting to read an assessment whether Turing Completeness is an advantage when including the security implications. – Murch Nov 3 '15 at 23:36
  • Actually there are primitive loops. They achieve safety by the inefficiency of the code size: files.acrobat.com/a/preview/… – MCCCS Jul 12 '18 at 8:46
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I Hope this primer guide helps

http://blockgeeks.com/guides/what-is-ethereum-a-step-by-step-beginners-guide/

At its simplest, Ethereum is an open software platform based on blockchain technology that enables developers to build and deploy decentralized applications.

Is Ethereum similar to Bitcoin? Well, sort of, but not really.

Like Bitcoin, Ethereum is a distributed public blockchain network. Although there are some significant technical differences between the two, the most important distinction to note is that Bitcoin and Ethereum differ substantially in purpose and capability. Bitcoin offers one particular application of blockchain technology, a peer to peer electronic cash system that enables online Bitcoin payments. While the bitcoin blockchain is used to track ownership of digital currency (bitcoins), the Ethereum blockchain focuses on running the programming code of any decentralized application.

In the Ethereum blockchain, instead of mining for bitcoin, miners work to earn Ether, a type of crypto token that fuels the network. Beyond a tradeable cryptocurrency, Ether is also used by application developers to pay for transaction fees and services on the Ethereum network.

What is a smart contract?

Smart contract is just a phrase used to describe computer code that can facilitate the exchange of money, content, property, shares, or anything of value. When run on the blockchain a smart contract becomes like a self-operating computer program that automatically executes when specific conditions are met. Because smart contracts run on the blockchain, they run exactly as programmed without any possibility of censorship, downtime, fraud or third party interference.

What are smart contract. A beginners guide

While all blockchains have the ability to process code, most are severely limited. Ethereum is different. Rather than giving a set of limited operations, Ethereum allows developers to create whatever operations they want. This means developers can build thousands of different applications that go way beyond anything we have seen before.

What is Blockchain Technology? A step-by-step guide than anyone can understand

The Ethereum Virtual Machine Before the creation of Ethereum, blockchain applications were designed to do a very limited set of operations. Bitcoin and other cryptocurrencies, for example, were developed exclusively to operate as peer-to-peer digital currencies.

Developers faced a problem. Either expand the set of functions offered by Bitcoin and other types of applications, which is very complicated and time-consuming, or develop a new blockchain application and an entirely new platform as well. Recognizing this predicament, Ethereum’s creator, Vitalik Buterin developed a new approach.

What is Blockchain Technology? A step-by-step guide than anyone can understand

Ethereum’s core innovation, the Ethereum Virtual Machine (EVM) is a Turing complete software that runs on the Ethereum network. It enables anyone to run any program, regardless of the programming language given enough time and memory. The Ethereum Virtual Machine makes the process of creating blockchain applications much easier and efficient than ever before. Instead of having to build an entirely original blockchain for each new application, Ethereum enables the development of potentially thousands of different applications all on one platform.

What can Ethereum be used for? Ethereum enables developers to build and deploy decentralized applications. A decentralized application or Dapp serves some particular purpose to its users. Bitcoin, for example, is a Dapp that provides its users with a peer to peer electronic cash system that enables online Bitcoin payments. Because decentralized applications are made up of code that runs on a blockchain network, they are not controlled by any individual or central entity.

What is Ethereum? A Step-by-Step Beginners Guide

Any services that are centralized can be decentralized using Ethereum. Think about all the intermediary services that exist across hundreds of different industries. From obvious services like loans provided by banks to intermediary services rarely thought about by most people like title registries, voting systems, regulatory compliance and much more.

Ethereum can also be used to build Decentralized Autonomous Organizations (DAO). A DAO is fully autonomous, decentralized organization with no single leader. DAO’s are run by programming code, on a collection of smart contracts written on the Ethereum blockchain. The code is designed to replace the rules and structure of a traditional organization, eliminating the need for people and centralized control. A DAO is owned by everyone who purchases tokens, but instead of each token equating to equity shares & ownership, tokens act as contributions that give people voting rights.

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