Zero K proof that a chess position contains a checkmate

In summary, a Zero K proof is a mathematical method used to verify that a given chess position contains a checkmate. This proof involves breaking down the game of chess into a series of logical statements and using mathematical principles to demonstrate that there is no possible move for the losing player to escape checkmate. This method provides a definitive and indisputable way to confirm the presence of checkmate in a chess position, making it a valuable tool for both players and chess enthusiasts.
  • #1
fluidistic
Gold Member
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Hi people,
It's been years I wanted to post this question here. I would like to build a zero knowledge proof that a given chess position contains at least one checkmate. I know that anything provable admits a zero k proof. I know about https://crypto.stackexchange.com/questions/110939/zero-knowledge-proof-applied-to-a-chess-position and .
I know it's been done already (see https://github.com/risc0/risc0/tree/main/examples/chess):
This code demonstrates a minimal example of how to use the RISC Zero zkVM to make ZK proofs about chess.


The demo uses the shakmaty crate to prove that a chess position has a checkmate without revealing what that checkmate is.
But I would like to understand exactly how to do so, every single step. There are other ways to accomplish it. I think I should be able to transform the problem into a graph/map with 3 colors scheme. I.e. if I can convince the Verifier that I can color the map with 3 colors such that no 2 colors are adjacent, then the proof would be complete. The hard part I don't know how to do is to apply an algorithm to transform a given FEN (or chess position) into such a graph. For example, this position
Code:
6Q1/8/8/8/8/8/5K2/7k w - - 0 1
contains 4 ways to checkmate in 1.
 
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  • #2
You need to feed the FEN into a chess engine, and get it to tell you what all of the legal moves are and what the resulting positions are.
 
  • #3
pasmith said:
You need to feed the FEN into a chess engine, and get it to tell you what all of the legal moves are and what the resulting positions are.
Not exactly. I could use shakmaty (not even a,chess engine) like risc0 does, to assert whether the FEN contains a checkmate. You don't even need to invoke the command to check all legal moves. However risc0 does more than this, for it is designed to be a real 0k setup. It's over my,head for now.
 

FAQ: Zero K proof that a chess position contains a checkmate

```html

What is "Zero K proof" in the context of chess?

"Zero K proof" in chess refers to a formal, mathematical proof that a particular chess position inevitably leads to a checkmate, regardless of the moves made by the players. This proof is constructed using logical deductions and the rules of chess to show that one side has a forced checkmate.

How does a "Zero K proof" differ from other types of chess analysis?

Unlike heuristic or empirical methods of chess analysis, a "Zero K proof" is a rigorous, mathematical demonstration that a position leads to checkmate. It leaves no room for error or interpretation, as it systematically proves that checkmate is unavoidable.

Can "Zero K proof" be applied to any chess position?

In theory, a "Zero K proof" can be applied to any chess position, but in practice, it is often used for endgames or specific tactical situations where a checkmate is imminent. Proving a checkmate from a complex middle-game position can be extremely challenging due to the vast number of possible moves and variations.

What tools or methods are used to create a "Zero K proof"?

Creating a "Zero K proof" typically involves a combination of human expertise and computer algorithms. Chess engines and databases can help identify critical positions and possible moves, while formal proof techniques in mathematics are used to establish the inevitability of checkmate.

Why is "Zero K proof" important in chess?

"Zero K proof" is important because it provides absolute certainty about the outcome of a position, which is valuable for both theoretical studies and practical play. It helps in understanding the depth and complexity of chess, and can also contribute to the development of stronger chess engines and algorithms.

```

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