If string(variable formula) is propositional formula, function canConvolutionFormula(formula) will return "true"

propositionalFormulaChecker.js

function canConvolutionFormula(formula){
    var replaceForSubFormula = "A";
    var atomOrConst = "([A-Z]|[0-1])";
    var atomOrConstInPatter = "<ATOM_OR_CONST>";
    var regFormula = "([(][!]<ATOM_OR_CONST>[)])|([(]<ATOM_OR_CONST>((&)|(\\|)|(->)|(~))<ATOM_OR_CONST>[)])";
    regFormula = regFormula.replace(new RegExp(atomOrConstInPatter, 'g'), atomOrConst);
    regFormula = new RegExp(regFormula);
    var oldFormula;

    do {
        oldFormula = formula;
        formula = formula.replace(regFormula, replaceForSubFormula);   
    } while (formula != oldFormula);

    var arrOutput = formula.match(new RegExp(atomOrConst, 'g'));
    if ((formula.length == 1) && (arrOutput != null) && (arrOutput.length == 1)) {
        return true;
    } else {
        return false;
    }
}