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docs/lsta_description.md

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@@ -6,7 +6,7 @@ Since the underlying structure of a set of quantum states is still an NFTA in Au
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This section is responsible for specifying a set of root states. It should contain only one line starting with "Root States" and ending with a set of root states separated by whitespaces.
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### # Transitions
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This section is responsible for specifying a set of transitions. One transition per line. Notice that the extension name `*.lsta` stands for Level-Synchronized (Nondeterministic Finite) Tree Automata which means that each transition is associated with a nonnegative integer denoting a set of choices in AutoQ. A (bottom-up) transition $f(q_1, q_2, ..., q_n) \to q$ associated with a set of choices $C$ is written as `[f,C](q1, q2, ..., qn) -> q`. Each pair of transitions `[f1,C1](...) -> q` and `[f2,C2](...) -> q` with the same `q` must satisfy $C_1 \& C_2 = 0$. In each layer of all used transitions for an accepted quantum state, the bitwise $\&$ of all used $C$'s must be positive. In this tool, a symbol can only be a positive integer $i$ with arity $2$ for specifying the $i$-th qubit or any expression describing a complex number with arity $0$ for specifying the amplitude of some computational basis states.
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This section is responsible for specifying a set of transitions. One transition per line. Notice that the extension name `*.lsta` stands for Level-Synchronized (Nondeterministic Finite) Tree Automata which means that each transition is associated with a nonnegative integer denoting a set of choices in AutoQ. A (bottom-up) transition $f(q_1, q_2, ..., q_n) \to q$ associated with a set of choices $C$ is written as `[f,C](q1, q2, ..., qn) -> q`. Each pair of transitions `[f1,C1](...) -> q` and `[f2,C2](...) -> q` with the same `q` must satisfy $C_1 \\& C_2 = 0$. In each layer of all used transitions for an accepted quantum state, the bitwise $\\&$ of all used $C$'s must be positive. In this tool, a symbol can only be a positive integer $i$ with arity $2$ for specifying the $i$-th qubit or any expression describing a complex number with arity $0$ for specifying the amplitude of some computational basis states.
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We close this section with the following example.
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```
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p1 ^ 2 < 1/8
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imag(p2) = 0
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p2 ^ 2 > 7/8
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```
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```

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