Abstract
In this chapter, we will study circuits over a structure whose domain is the set Γ ∗ of all finite words over a finite alphabet. The operations used in the circuit include the binary concatenation and all symbols from Γ as constants. Such circuits are also called straight-line programs (SLPs). A straight-line program can be also viewed as a context-free grammar [82] that produces only a single word. Note that, as remarked in Sect. 1.3.7, the term “straight-line program” is also used for arithmetic circuits. In this book, we use the term “straight-line program” exclusively for circuits over free monoids. We will also consider extensions of straight-line programs, where some additional operations on words may be used in circuits (the so-called CSLPs and PCSLPs).
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