Using Colored Petri Net for Accounting System

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This entry is adapted from the peer-reviewed paper 10.3390/computers10120169

Many learners who are not familiar with the accounting terms find blended learning very complex to understand with respect to the computerized accounting system, the journal entries process, and tracing the accounting transaction flows of accounting system. A simulation-based model is a viable option to help instructors and learners make understanding the accounting system components and monitoring the accounting transactions easier. This entry briefly introduce a colored Petri net (CPN)-based model.

computerized accounting system colored Petri net (CPN)

1. Background

Petri-net-based techniques have been used in computer science to validate a concurrent system. There is no research that directly provides a Petri-net-based technique for an instruction of the accounting system. This entry describes the accounting software, and the researches that proposes the Petri-net-based techniques in computer science and business process domain.

2. Computer-Aided Instruction and Accounting Information Systems

Computer-aided instruction or computer-assisted instruction (CAI) ^[1] is an interactive instructional multimedia for increasing a learner’s understanding and allowing the learners to proceed at their own pace. CAI is used in various disciplines and is accordingly designed with respect to the objectives and resources of a course. It record-keeps, progresses tracking, and assesses the learner performance. The CAI program comprises the representations of course contents and their extension, including drilling, practicing, and simulating tutorials and activities. Multimedia of the CAI program can be applied in studying the fundamental accounting and develops accounting skills in problem solving.

An accounting system is the system that manages the organization’s financial information. This paper focuses on the computerized accounting system or the accounting information system (AIS) ^[2]. The cycle of the accounting system is shown in Figure 1. The accounting process starts at the journal entry module, which is an accounting treatment operated accordingly to the principle of double-entry accounting ^[3]. A chart of accounts ^[2] is a list of financial accounts that is set up for mapping the raw financial data or business transaction into the accounting transactions. A ledger contains a list of accounting transactions derived from the journal entries. A ledger posting is a transforming process the Debit and Credit amounts in the journals into the corresponding ledger account. Next, the accountants may adjust the account at the end of account period, and the financial report creation and the book closing or ledger closing are performed, respectively. Essentially, AIS provides the seven core modules as follows:

Figure 1. The cycle of accounting system.

Point of sale module (POS module): this represents the place where the raw financial transactions takes place. The financial transactions may be posted by hand or automated by an integrated POS module. In the integrated POS module, the account mapping profile is used to map the raw financial transactions into the accounting transactions.
Chart of account module or COA: A chart of accounts is manipulated at the COA module, on which the accounts in the list are classified into five series: assets, liabilities, equity, revenue, and expenses.
Accounts receivable module: accounts receivable handles the invoicing and manages the customer payments.
Accounts payable module: accounts payable handles the recording and tracking of the money owned by a business.
General ledger module: the general ledger module is responsible for consolidating the accounting information from the point of sale module, accounts receivable module, and accounts payable module. Financial reports are computed from the accounting transactions stored in the general ledger module, and these transactions may be used for auditing purposes.
Trial balance module: the trial balance module shows a listing of accounts that come along with the net balance of each account. It is useful for an internal checking because a trial balance can disclose the net balance both before adjustment and after adjustment, and it comprises the primary data for creating the balance sheet, income statement and cash flow report.
Balance sheet module: this details a list of the organization assets, liabilities, and equity. It also be used to create and estimate the clash flow budget.

Although there are educational software licenses of accounting system for students, the tracing of accounting transaction flows and the checking of transformations of raw financial data into the accounting transaction can be consolidated and verified by data inspection on the finalized financial reports only. It is better for the learners to be able to interact with the accounting system simulation step-by-step, and arbitrarily trace and monitor the transaction flows and the data objects in each accounting situation.

3. Colored Petri Net

Colored Petri net ^[4] or CPN is a mathematical modeling language for model checking ^[5]. It has been used for modeling and verifying the concurrent and distributed systems in various disciplines such as computer science, biology, and chemistry. CPN is combination of the discrete event dynamic system of classical Petri net and programming language, providing useful properties to allow the distinction between tokens. The core elements of a CPN model and PT model are alike. A place is an elliptical circle used for representation of a system state. A transition is a rectangle that represents an action or event of a system. An arc connects between a place and transition to show the direction of process flows. The state change is represented by the token’s movement from a place to another place(s) by using the arc(s) crossing the transition. This action is called “transition firing”. In the CPN modeling tool, a color set and variable declaration including an inscription expression must conform to the syntax and lexicon of the back-end programming language of the modeling tool used.

Figure 2a shows the core CPN elements, and Figure 2b shows an example of the CPN model of the simple protocol that represents six data packages that are transmitted from the sender to the receiver through the network protocol. The transition “Send Packet” is enabled and it will fire one by one token to the place “A”, these events represent that the sender sends a message through the network protocol. Next, the transition “Transmit Packet” will fire a token to the place “B”, demonstrating the message transmission to the receiver by the network protocol. Last, the transition “Receive Packet” consumes a token from the place “B” and fires two tokens to the place “Packets Received” and “C”, displaying that the receiver gets the message. The receiver will acknowledge the sender via the network protocol with the transition firing of the transition “Transmit Act”. However, this CPN model does not consider the message ordering, re-transmitting, and lost message.

Figure 2. (a) Core elements of CPN. (b) Example of CPN model of a simple protocol.

CPN modeling tools usually provide a simulation mode and verification mode. The simulation mode works under a particular scenario, whereas the verification mode works on all possible states. To analyze a state space in verification mode, the state space generator and temporal logic ^[6] are provided. However, the state space explosion problem ^[7] remains a drawback of verification mode if the CPN model has behaviors that are large in size or complex.

There are many works ^[8]^[9]^[10]^[11]^[12], not only in computer science, that use Petri nets for describing and simulating a system’s biology and chemical reactions. It allows scientists to design and analyze the biological system network, acid cycle, metabolic pathway, and system behaviors. However, a classical Petri net cannot describe the low-level system behaviors. Thus, height-level Petri nets such as colored qualitative Petri net (QPNC), colored stochastic Petri net (SPNC), and colored continuous Petri net have recently applied to model and analyze biological systems.

References

Collins, D.; Deck, A.; McCrickard, M. Computer aided instruction A study of student evaluations and academic performance. J. Coll. Teach. Learn. 2008, 5, 49–58.
Cooper, J.P.; Pattanayak, S. Chart of Accounts: A Critical Element of the Public Financial Management Framework; Citeseer: Princeton, NJ, USA, 2011.
Bryer, R.A. Double-entry bookkeeping and the birth of capitalism: Accounting for the commercial revolution in medieval northern Italy. Crit. Perspect. Account. 1993, 4, 113–140.
Jensen, K.; Kristensen, L.M.; Wells, L. Coloured Petri Nets and CPN Tools for modelling and validation of concurrent systems. Int. J. Softw. Tools Technol. Transf. 2007, 9, 213–254.
Baier, C.; Katoen, J.P. Principles of Model Checking; MIT Press: Cambridge, MA, USA, 2008.
Fisher, M. An Introduction to Practical Formal Methods Using Temporal Logic; John Wiley & Sons: Hoboken, NJ, USA, 2011; Volume 82.
Clarke, E.M.; Klieber, W.; Nováček, M.; Zuliani, P. Model checking and the state explosion problem. In LASER Summer School on Software Engineering; Springer: Berlin/Heidelberg, Germany, 2011; pp. 1–30.
Koch, I. Petri nets in systems biology. Softw. Syst. Model. 2015, 14, 703–710.
Blätke, M.A.; Heiner, M.; Marwan, W. Petri Nets in Systems Biology; Technical Report; Otto von Guericke University Magdeburg: Magdeburg, Germany, 2011.
Pinney, J.W.; Westhead, D.R.; McConkey, G.A. Petri Net representations in systems biology. Biochem. Soc. Trans. 2003, 31, 1513–1515.
Heiner Monika, D.G.; Donaldson, R. Petri nets for systems and synthetic biology. In Proceedings of the International School on Formal Methods for the Design of Computer, Communication and Software Systems, Bertinoro, Italy, 2–7 June 2008; pp. 215–264.
Liu, F. Colored Petri Nets for Systems Biology. Master’s Thesis, Brandenburg University of Technology, Cottbus, Germany, 2012.

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Chanon Dechsupa

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1. Background

2. Computer-Aided Instruction and Accounting Information Systems

3. Colored Petri Net

References