“These boards have become the new censors,” said Wesley Hottot, an Institute for Justice lawyer who is representing Mr. Jarlstrom. “They think that the First Amendment does not apply to them.”

Eric Engelson, communications coordinator for the Oregon board, said the board would not comment since the litigation was pending. The board, a semi-independent panel whose members are appointed by the governor, funds itself through licensing and registration fees.

Mr. Jarlstrom does not have an engineering license issued by the state board. He is a self-employed consultant who tests audio products and repairs, upgrades and calibrates test instruments. But he did earn a bachelor’s degree in electronics engineering in Sweden, where he was born. He has also spent a couple of years researching traffic light timing intervals, which included consulting with one of authors of the original 1959 mathematical formula used as a basis for programming traffic light signals.

Nonetheless, the Oregon board, after a nearly two-year investigation, assessed a $500 civil penalty because Mr. Jarlstrom called himself “an excellent engineer” in one of several emails to the board and informed the Washington County sheriff that he “invented and publicly released a new extended solution” to the problem of yellow lights in traffic flow.

The board explained it had “opened a law enforcement case” against Mr. Jarlstrom “for the unlicensed practice of engineering,” and cited his attempts to publicize his review, critique and recalculations of the current formulas in use.

“This is a broad pattern of this board,” Mr. Hottot said, adding that he has seen similar actions other states.

Last year, for example, the Oregon board opened an investigation into Allen Alley, the Republican candidate for governor, because a political ad stated: “I’m an engineer and a problem solver.” Although Mr. Alley has a mechanical engineering degree from Purdue University and worked as an engineer for Ford and Boeing, the board said that he was not registered in Oregon as a professional engineer.