I don't know how you can be more non-technical than that except by saying 'turing complete means 'able to answer computable problem given enough time and space''.

There are more exotic systems that can still achieve everything a Turing machine can, which makes them Turing complete too: If your language has infinite random access memory, conditional execution, and some form of repeated execution, it's probably Turing complete. If you had a language that was forbidden from implementing a Python interpreter, it wouldn't be Turing complete. A Turing machine can use its random access memory to track ()'s and 's separately, but this language with only a stack cannot.ДЄ Turing machine can simulate any other Turing machine - A Turing machine, when given an appropriate 'program', can take another Turing machine's 'program' and simulate it on arbitrary input. However, it can't tell me if every ( has its own ) later on and every later on (note that ( meets this criteria but (] does not).

If I have a 'language' that reads a string once and can only use memory by pushing and popping from a stack, it can tell me whether every ( in the string has its own ) later on by pushing when it sees ( and popping when it sees ). This is one reason regular expressions aren't Turing complete.ДЄ Turing machine has random access memory - A language that only lets you work with memory through push and pop operations to a stack wouldn't be Turing complete. This is why we can't actually build a Turing machine, but Java is still a Turing complete language because the Java language has no restriction preventing it from using infinite memory. Coq is a theorem prover that can't express programs that don't terminate, so it's not Turing complete.ДЄ Turing machine can use infinite memory - A language that was exactly like Java but would terminate once it used more than 4 Gigabytes of memory wouldn't be Turing complete, because a Turing machine can use infinite memory. Things that can make a language NOT Turing completeДЄ Turing machine can make decisions based on what it sees in memory - The 'language' that only supports +, -, *, and / on integers is not Turing complete because it can't make a choice based on its input, but a Turing machine can.ДЄ Turing machine can run forever - If we took Java, Javascript, or Python and removed the ability to do any sort of loop, GOTO, or function call, it wouldn't be Turing complete because it can't perform an arbitrary computation that never finishes. The input to a Turing machine is put in its memory before it starts. A Turing machine is a machine with infinite random access memory and a finite 'program' that dictates when it should read, write, and move across that memory, when it should terminate with a certain result, and what it should do next. The Church-Turing Thesis states that any performable computation can be done by a Turing machine. Update: You can learn more on my blog post: 'JavaScript Is Turing Complete'вЂЉ-вЂЉExplainedДЄ Turing complete language is one that can perform any computation. Java, JavaScript, Perl, etc.) are all Turing complete because they each implement all the features required to run programs like addition, multiplication, if-else condition, return statements, ways to store/retrieve/erase data and so on. On the other hand, if it can run any program that the universal Turing machine can run, then it's Turing complete. This would make it 'Turing incomplete' (so to speak).

But now imagine that for some reason your programming language can't perform the same addition. A Turing machine can easily run this program. Now, a programing language is called 'Turing complete', if it can run any program (irrespective of the language) that a Turing machine can run given enough time and memory.ДЇor example: Let's say there is a program that takes 10 numbers and adds them. Programming languages are similar to those machines (although virtual). So he created 'Universal Turing Machine' that can take ANY program and run it. But then he had to create different machines for different programs. Alan Turing created a machine that can take a program, run that program, and show some result.

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