Relational semigroups with domain and range are a useful tool for modelling nondeterministic programs. We prove that the representation class $R(D,R,*)$ is not finitely axiomatisable, answering arXiv:1811.01712 Question 5.1. We show that any signature containing $D, R, \smile, ;$ but not $-$ or $\cdot$ has the finite representation property, an extension of the result for ordered domain algebras $\{0,1,D,R, \leq, 1', \smile,;\}$. We survey the results in the area of the finite representation property and raise a number of open questions.

翻译：具有域域和范围的半关系组是模拟非确定性程序的一个有用工具。 我们证明,代表等级$R(D,R,*)并非可有一定的必然性,回答问题5.1. 我们显示,任何包含$D、R、\smile的签名;但美元或美元以外的签名都具有有限代表属性,是订购域代数$0,1,D,R、\leq、1',\smile的结果的延伸; ⁇ $。 我们调查了有限代表属性领域的结果,并提出了一些未决问题。