rstm

---

Welcome to rstm, this crate is dedicated to establishing a robust framework for Turing machines in Rust. The crate defines various components, actors, and macros aimed at facilitating the creation and execution of Turing machines.

Overview

rstm provides a comprehensive suite of tools for defining and working with Turing machines.

Rules

At the core of any Turing machine lies its set of rules, which dictate how the machine transitions between states based on the symbols it reads from its tape. In rstm, a rule is represented by the following structure:

    pub struct Rule<Q, A> {
        pub head: Head<Q, A>,
        pub tail: Tail<Q, A>,
    }

where the Head is defined as:

    pub struct Head<Q, A> {
        pub state: Q,
        pub symbol: A,
    }

and the Tail is defined as:

    pub struct Tail<Q, A> {
        pub direction: Direction,
        pub next_state: Q,
        pub write_symbol: A,
    }

Serialization

Enabling the serde feature will allow for serialization and deserialization of the Rule and other implementations within the crate. That being said, the serialization of the Rule macro is notable for the fact that it flattens both the head and tail fields, resulting in a more compact representation.

rule!, ruleset!, and other rule-based macros

Researchers have simplified the definition of a Turing machine, boiling it down into a dynamical system defined by a set of states, symbols, and rules. The rules define the behavior of the machine, dictating how it transitions from one state to another based on the current symbol being read. More specifically, the transition function $\delta$ where:

$$ \delta: Q\times{A}\rightarrow{Q}\times{A}\times{\lbrace\pm{1},0\rbrace} $$

as defined within the paper On the Topological Dynamics of Turing Machines by Petr Kůrka. Therefore, we allow any rule-based procedural macros within the scope of rstm to follow the following syntax:

(state, symbol) -> Direction(next_state, next_symbol)

Note: the macros are hygenic, in the fact that they do not require the user to import any variants, traits, or other types into scope.

Examples

For more examples visit the examples directory.

Example #1: Using the rule! macro

The following example demonstrates the use of the rule! macro to define a single rule:

    rstm::rule! { (0, 0) -> Right(1, 0) }

Example #2: Using the ruleset! macro

The following example demonstrates the use of the rules! macro to define a set of rules:

    rstm::ruleset! {
        (0, 0) -> Right(1, 0),
        (0, 1) -> Stay(-1, 1),
        (1, 0) -> Left(0, 1),
        (1, 1) -> Right(-1, 0),
        (-1, 0) -> Right(0, 0),
        (-1, 1) -> Right(1, 1),
    }

Example #3: Using the program! macro

The following example demonstrates the use of the program! macro to define a set of rules for a three-state, two-symbol Turing machine.

    // define the ruleset for the machine
    rstm::program! {
        #[default_state(0)] // optional
        rules: {
            (0, 0) -> Right(1, 0),
            (0, 1) -> Stay(-1, 1),
            (1, 0) -> Left(0, 1),
            (1, 1) -> Right(-1, 0),
            (-1, 0) -> Right(0, 0),
            (-1, 1) -> Right(<i8>::MAX, 1),
        };
    }

Example #4: Putting it all together with the TMH implementation

    extern crate rstm;

    use rstm::Head;

    fn main() -> rstm::Result<()> {
        // initialize the logger
        tracing_subscriber::fmt()
            .with_max_level(tracing::Level::TRACE)
            .with_target(false)
            .with_timer(tracing_subscriber::fmt::time::uptime())
            .init();
        tracing::info!("Welcome to rstm!");
        // define some input for the machine
        let input = [0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0];
        // initialize the state of the machine
        let initial_state: isize = 0;
        // define the ruleset for the machine
        let program = rstm::program! {
            #[default_state(initial_state)]
            rules: {
                (0, 0) -> Right(1, 0),
                (0, 1) -> Left(-1, 1),
                (1, 0) -> Right(0, 1),
                (1, 1) -> Right(-1, 0),
                (-1, 0) -> Left(<isize>::MAX, 0),
                (-1, 1) -> Left(1, 1),
            };
        };
        // create a new instance of the machine
        let mut tm = Head::new(initial_state, 0usize).load(program);
        // load the input into the machine tape
        tm.extend_tape(input);
        // execute the program
        tm.run()
    }

Getting Started

For a more detailed guide on getting started, please refer to the QUICKSTART.md file.

Building from the source

To build the project from source, start by cloning the repository:

git clone https://github.com/FL03/rstm.git

before switching into the project directory:

cd rstm

and building the project targeting the desired feature set:

cargo build --workspace --features default

Run an example

cargo run -f F --example {actor}

Usage

To add rstm to your Rust project, run the following command:

cargo add rstm --features macros

or, manually include it in your Cargo.toml file as such:

[dependencies.rstm]
version = "0.1.x"
features = [
    "default",
]

Contributing

Contributions are welcome! For more information visit the CONTRIBUTING.md file.