FSA接受的语言联盟，没有epsilon过渡

Question

我一直试图在没有使用epsilon转换的情况下形式化两个有限状态自动机的并集。我想为新的自动机创建一个新的初始启动状态，并从这个新的启动状态通过复制这些转换创建从单独的自动机的启动状态转换到可达状态。

鉴于FSA

def donation_application(request):
    if request.method == 'POST':
        form = DirectDonationForm(data=request.POST)
        if form.is_valid():
            stripe.api_key = settings.STRIPE_SECRET_KEY
            name = request.POST.get('name', '')
            address = request.POST.get('address', '')
            city = request.POST.get('city', '')
            state = request.POST.get('state', '')
            zip = request.POST.get('zip', '')
            phone_number = request.POST.get('phone_number', '')
            support = request.POST.get('support', '')
            agree = request.POST.get('agree', '')
            email_address = request.POST.get('email_address', '')
            number = request.POST.get('number', '')
            cvc = request.POST.get('cvc', '')
            exp = request.POST.get('exp', '')
            # token = form.cleaned_data['stripe_token'],
            # exp_m = int(request.POST.get('exp_month', ''))
            # exp_y = int(request.POST.get('exp_year', ''))

            exp_month = exp[0:2]
            exp_year = exp[5:9]

            subject = 'New Donation'
            from_email = settings.DEFAULT_FROM_EMAIL
            recipient_list = ['deniselarkins@/////\\\\\.com',
                              'charles@/////\\\\\.net',
                              'marcmunic@/////\\\\\.com',
                              ]

            token = stripe.Token.create(
                card={
                    'number': number,
                    'exp_month': exp_month,
                    'exp_year': exp_year,
                    'cvc': cvc
                },
            )

            customer = stripe.Customer.create(
                email=email_address,
                source=token,
            )

            total_support = decimal.Decimal(support) / 100
            total_charge = decimal.Decimal(int(support)) / 100

            # Charge the user's card:
            charge = stripe.Charge.create(
                amount=total_charge,
                currency='usd',
                description='Donation',
                customer=customer.id
            )

            ctx = {
                'name': name,
                'address': address,
                'city': city,
                'state': state,
                'zip': zip,
                'phone_number': phone_number,
                'email_address': email_address,
                'agree': agree,
                'charge': charge,
                'customer': customer,
                'total_support': total_support,
                'total_charge': total_charge
            }

            message = get_template('email_forms/direct_donation_form_email.html').render(Context(ctx))
            msg = EmailMessage(subject, message, from_email=from_email, to=recipient_list)
            msg.content_subtype = 'html'
            msg.send(fail_silently=True)

            return redirect(
                '/contribute/donation-support-thank-you/?name=' + name +
                '&address=' + address +
                '&state=' + state +
                '&city=' + city +
                '&zip=' + zip +
                '&phone_number=' + phone_number +
                '&email_address=' + email_address +
                '&total_support=' + str(total_support) +
                '&total_charge=' + str(total_charge)
            )
    context = {
        'title': 'Donation Pledge',
    }

    return render(request, 'contribute/_donation-application.html', context)

其中Σ1=字母，Q_1是状态集，q0_1是开始状态， - ＆gt; _1是M1的转变。

鉴于另一个FSA

M1 = <Σ1, Q_1, q0_1, ->_1> 

其中Σ2是字母表，Q_2是状态集合，q0_2是开始状态， - ＆gt; _2是M2的转变。

现在我已将FSA M + =M1∪M2定义为FSA：

 M2 = <Σ2, Q_2, q0_2, ->_2>  

我一直在发现定义问题 - ＆gt; _C - 新的过渡到M1和M2的可达状态。我将 - ＆gt; _C的类型定义如下：Q x 2 ^Σx2 ^ Q. 它必须是一套，但我不确定如何正式定义它。任何帮助将非常感谢。