I don’t like the word programming languages. Even though digital VLSI designers cod in an HDL (verilog, VHDL, systemverilog), it is hardware that they implement, not software. It looks software but in fact it isn’t. There are limitations on the operators and constructs that a synthesis tool can infer from a HDL file. Thus a digital HW designer is somebody that knows about digital (synchronous) logic and the relationship between HDL and the resulting hardware. Hardware designers also use Tcl (some EDA tools have tcl scripts as input), shell scripts and Python or Perl. These scripts are used to run command line tools and to process input or output (log) files. or to start and check regressions, … . For the embedded software (firmware), C or C++ is commonly used.
What programming languages do VLSI industries use?