Algorithms of process discovery help analysts to understand business processes and problems in a system by creating a process model based on a log of the system. There are existing algorithms of process discovery, namely graph-based. Of all algorithms, there are algorithms that process graph-database to depict a process model. Those algorithms claimed that those have less time complexity because of the graph-database ability to store relationships. This research analyses graph-based algorithms by measuring the time complexity and performance metrics and comparing them with a widely used algorithm, i.e. Alpha Miner and its expansion. Other than that, this research also gives outline explanations about graph-based algorithms and their focus issues. Based on the evaluations, the graph-based algorithm has high performance and less time complexity than Alpha Miner algorithm.

http://ijain.org/index.php/IJAIN/article/download/296/ijain_v5i2_p137-149

A survey of graph-based algorithms for discovering business processes

There is a rich variety of shuffling operations ranging from asynchronous interleaving to various forms of synchronizations. We introduce a general shuffling operation which subsumes earlier forms of shuffling. We further extend the notion of a Brzozowski derivative to the general shuffling operation and thus to many earlier forms of shuffling. This extension enables the direct construction of automata from regular expressions involving shuffles that appear in specifications of concurrent systems.

/pdf/derivatives-for-regular-shuffle-expressions-29axqx56mk.pdf

Derivatives for Regular Shuffle Expressions

In this paper we investigate how it is possible to recover an automaton from a rational expression that has been computed from that automaton. The notion of derived term of an expression, introduced by Antimirov, appears to be instrumental in this problem. The second important ingredient is the co-minimization of an automaton, a dual and generalized Moore algorithm on non-deterministic automata. If an automaton is then sufficiently decorated, the combination of these two algorithms gives the desired result. Reducing the amount of decoration is still the object of ongoing investigation.

How expressions can code for automata

Derivatives and partial derivatives for regular shuffle expressions

In earlier work [LMP11], we showed that a graph-theoretic condition called “structural cyclicity” enables us to extract syntax from a conflict-equivalent product system of automata. In this paper we have a “pairing” property in our syntax which allows us to connect to a broader class of product systems, where the conflict-equivalence is not statically fixed. These systems have been related to labelled free choice nets.

/pdf/kleene-theorems-for-labelled-free-choice-nets-1y6n0uyvcr.pdf

Kleene Theorems for Labelled Free Choice Nets.

Two of the most celebrated results that effectively exploit visual representation to give logical characterization and decidable model-checking include visibly pushdown automata (VPA) by Alur and Madhusudan and event-clock automata (ECA) by Alur, Fix and Henzinger. VPA and ECA—by making the call-return edges visible and by making the clock-reset operation visible, respectively—recover decidability for the verification problem for pushdown automata implementation against visibly pushdown automata specification and timed automata implementation against event-clock timed automata specification, respectively. In this work we combine and extend these two works to introduce dense-time visibly pushdown automata that make both the call-return as well as resets visible. We present MSO logic characterization of these automata and prove the decidability of the emptiness problem for these automata paving way for verification problem for dense-timed pushdown automata against dense-timed visibly pushdown automata specification.

A Logical Characterization for Dense-Time Visibly Pushdown Automata

We prove Kleene theorems for two subclasses of labelled product systems which are inspired from well-studied subclasses of 1- bounded Petri nets. For product T-systems we define a corresponding class of expressions. The algorithms from systems to expressions and in the reverse direction are both polynomial time. For product free choice systems with a restriction of structural cyclicity, that is, the initial global state is a feedback vertex set, going from systems to expressions is still polynomial time; in the reverse direction it is polynomial time with access to an NP oracle for finding deadlocks.

Kleene theorems for product systems

Perfect languages--a term coined by Esparza, Ganty, and Majumdar--are the classes of languages that are closed under Boolean operations and enjoy decidable emptiness problem. Perfect languages form the basis for decidable automata-theoretic model-checking for the respective class of models. Regular languages and visibly pushdown languages are paradigmatic examples of perfect languages. Alur and Dill initiated the language-theoretic study of timed languages and introduced timed automata capturing a timed analog of regular languages. However, unlike their untimed counterparts, timed regular languages are not perfect. Alur, Fix, and Henzinger later discovered a perfect subclass of timed languages recognized by event-clock automata. Since then, a number of perfect subclasses of timed context-free languages, such as event-clock visibly pushdown languages, have been proposed. There exist examples of perfect languages even beyond context-free languages:--La Torre, Madhusudan, and Parlato characterized first perfect class of context-sensitive languages via multistack visibly pushdown automata with an explicit bound on number of stages where in each stage at most one stack is used. In this paper we extend their work for timed languages by characterizing a perfect subclass of timed context-sensitive languages called dense-time multistack visibly pushdown languages and provide a logical characterization for this class of timed languages.

A Perfect Class of Context-Sensitive Timed Languages

In earlier work [LMP11], we showed that a graph-theoretic condition called "structural cyclicity" enables us to extract syntax from a conflict-equivalent product system of automata. In this paper we have a "pairing" property in our syntax which allows us to connect to a broader class of synchronous product systems [Arn94] with a "matching" property, where the conflict-equivalence is not statically fixed. These systems have been related to labelled free choice nets.

Ramchandra Phawade

Papers

A Logical Characterization for Dense-Time Visibly Pushdown Automata

Kleene theorems for product systems

Kleene Theorems for Labelled Free Choice Nets.

A Perfect Class of Context-Sensitive Timed Languages

Kleene Theorems for Synchronous Products with Matching