# What is the "successive-configuration relation"?

This term is used in the book Foundations of Cryptography on pg 20 with regard to defining deterministic oracles, but is not previously defined and I can't seem to find a definition online easily.

Definition 1.3.8 (Oracle Machines): A (deterministic/probabilistic) oracle machine is a (deterministic/probabilistic) Turing machine with an additional tape, called the oracle tape, and two special states, called oracle invocation and oracle appeared. The computation of the deterministic oracle machine $M$ on input $x$ and with access to the oracle $f:\{0,1\}^*\to\{0,1\}^*$ is defined by the successive-configuration relation. For configurations with states different from oracle invocation, the next configuration is defined as usual. Let $\gamma$ be a configuration in which the state is oracle invocation and the content of the oracle tape is $q$. Then the configuration following $\gamma$ is identical to $\gamma$ , except that the state is oracle appeared, and the content of the oracle tape is $f(q)$. The string $q$ is called $M$’s query, and $f(q)$ is called the oracle reply. The computation of a probabilistic oracle machine is defined analogously. The output distribution of the oracle machine $M$, on input $x$ and with access to the oracle $f$ , is denoted $M^f(x)$.
Now if we look at the formal definition of a turing machine, we will spot a relation $\delta:(Q\setminus F)\times\Gamma\to Q\times \Gamma\times\{L,R\}$. Note how a function is actually just a relation.