A chaining bit decoder of a computer processor receives an instruction stream. The chaining bit decoder selects a group of instructions from the instruction stream. The chaining bit decoder extracts a designated bit from each instruction of the instruction stream to produce a sequence of chaining bits. The chaining bit decoder decodes the sequence of chaining bits. The chaining bit decoder identifies zero or more instruction stream dependencies among the selected group of instructions in view of the decoded sequence of chaining bits. The chaining bit decoder outputs control signals to cause one or more pipelines stages of the processor to execute the selected group of instructions in view of the identified zero or more instruction stream dependencies among the group sequence of instructions.