Query Checking Research Articles

Data-Aware Declarative Process Mining with SAT

Process Mining is a family of techniques for analyzing business process execution data recorded in event logs. Process models can be obtained as output of automated process discovery techniques or can be used as input of techniques for conformance checking or model enhancement. In Declarative Process Mining, process models are represented as sets of temporal constraints (instead of procedural descriptions where all control-flow details are explicitly modeled). An open research direction in Declarative Process Mining is whether multi-perspective specifications can be supported, i.e., specifications that not only describe the process behavior from the control-flow point of view, but also from other perspectives like data or time. In this article, we address this question by considering SAT (Propositional Satisfiability Problem) as a solving technology for a number of classical problems in Declarative Process Mining, namely, log generation, conformance checking, and temporal query checking. To do so, we first express each problem as a suitable FO (First-Order) theory whose bounded models represent solutions to the problem, and then find a bounded model of such theory by compilation into SAT.

ASP-Based Declarative Process Mining

We put forward Answer Set Programming (ASP) as a solution approach for three classical problems in Declarative Process Mining: Log Generation, Query Checking, and Conformance Checking. These problems correspond to different ways of analyzing business processes under execution, starting from sequences of recorded events, a.k.a. event logs. We tackle them in their data-aware variant, i.e., by considering events that carry a payload (set of attribute-value pairs), in addition to the performed activity, specifying processes declaratively with an extension of linear-time temporal logic over finite traces (LTLf). The data-aware setting is significantly more challenging than the control-flow one: Query Checking is still open, while the existing approaches for the other two problems do not scale well. The contributions of the work include an ASP encoding schema for the three problems, their solution, and experiments showing the feasibility of the approach.

A tableau construction for finite linear-time temporal logic

This paper gives a tableau-based technique for converting formulas in finite propositional linear-time temporal logic (Finite LTL) into finite-state automata whose languages are the models of the given formula. Finite LTL differs from traditional LTL in that formulas are interpreted with respect to finite, rather than infinite, sequences of states; this fact means that traditional finite-state automata, rather than ω-automata such as those developed by Büchi and others, suffice for recognizing models of such formulas. The approach presented here works by associating with each state in the constructed automaton a Finite LTL formula satisfied by the sequences that can be accepted by the automaton when started in the given state. Such tableau-construction techniques are well-known in the setting of traditional LTL, where they are used to construct ω-automata; we adapt here for the setting of Finite LTL and finite-state automata. The resulting automata may be used as a basis for model checking, model synthesis, query checking and satisfiability testing.

Parameterized Weighted Containment

Partially specified systems and specifications are used in formal methods such as stepwise design and query checking. Existing methods consider a setting in which systems and their correctness are Boolean. In recent years, there has been growing interest and need for quantitative formal methods, where systems may be weighted and specifications may be multivalued. Weighted automata, which map input words to a numerical value, play a key role in quantitative reasoning. Technically, every transition in a weighted automaton A has a cost, and the value A assigns to a finite word w is the sum of the costs on the transitions traversed along the most expensive accepting run of A on w . We study parameterized weighted containment : given three weighted automata A , B , and C , with B being partial, the goal is to find an assignment to the missing costs in B so that we end up with B ′ for which B ′≤ C , where ≤ is the weighted counterpart of containment. We also consider a one-sided version of the problem, where only A or only C is given in addition to B , and the goal is to find a minimal assignment with which A ≤ B ′ or, respectively, a maximal one with which B ′ ≤ C . We argue that both problems are useful in stepwise design of weighted systems as well as approximated minimization of weighted automata. We show that when the automata are deterministic, we can solve the problems in polynomial time. Our solution is based on the observation that the set of legal assignments to k missing costs forms a k -dimensional polytope. The technical challenge is to find an assignment in polynomial time even though the polytope is defined by means of exponentially many inequalities. We do so by developing a divide-and-conquer algorithm based on a separation oracle for polytopes. For nondeterministic automata, the weighted setting is much more complex, and in fact even nonparameterized containment is undecidable. We are able to show positive results for variants of the problems, where containment is replaced by simulation.

An abstraction-refinement framework for trigger querying

Trigger querying is the problem of finding, given a system M and an LTL formula φ, the set of scenarios that trigger φ in M; that is, the language L of finite computations of M such that all infinite computations that have a prefix in L continue with a suffix that satisfies φ. Trigger querying significantly extends query checking, which seeks propositional solutions, and is an extremely useful methodology for system exploration and understanding. The weakness of trigger querying lies in the fact that the size of the solution is linear in the size of the system. For trigger querying to become feasible in practice, we must offer solutions to cope with systems of big, and possibly infinite, state spaces. In this paper we describe an abstraction-refinement framework for trigger querying. Instead of reasoning about the system M, we reason about an abstraction of it and return to the user two languages that under- and over-approximate the language L of computations that trigger φ in M. We describe an automata-theoretic approach for refining and reducing the gap between the approximations and show how, unlike classical counterexample-based refinement approaches, here it is possible to symbolically handle batches of counterexamples. We show that our framework is robust and can be applied also for classical query checking as well as variants and extensions of trigger querying.

Multi-valued model checking games

This work extends the game-based framework of μ-calculus model checking to the multi-valued setting. In multi-valued model checking a formula is interpreted over a Kripke structure defined over a lattice. The value of the formula is also an element of the lattice. This problem has many applications in verification, such as handling abstract or partial models, analyzing systems in the presence of inconsistent views, and performing temporal logic query checking. We define a new game for the multi-valued model checking problem of the full μ-calculus, and demonstrate how to derive from it a direct model checking algorithm for its alternation-free fragment. The algorithm handles the multi-valued structure without any reduction. We investigate the properties of the new game, both independently, and in comparison to the automata-based approach. We show that the usual resemblance between the automata-based and the game-based approach does not hold in the multi-valued setting and show how it can be regained by changing the nature of the game.

LATTICED SIMULATION RELATIONS AND GAMES

Multi-valued Kripke structures are Kripke structures in which the atomic propositions and the transitions are not Boolean and can take values from some set. In particular, latticed Kripke structures, in which the elements in the set are partially ordered, are useful in abstraction, query checking, and reasoning about multiple view-points. The challenges that formal methods involve in the Boolean setting are carried over, and in fact increase, in the presence of multi-valued systems and logics. We lift to the latticed setting two basic notions that have been proven useful in the Boolean setting. We first define latticed simulation between latticed Kripke structures. The relation maps two structures M1 and M2 to a lattice element that essentially denotes the truth value of the statement "every behavior of M1 is also a behavior of M2". We show that latticed-simulation is logically characterized by the universal fragment of latticed µ-calculus, and can be calculated in polynomial time. We then proceed to defining latticed two-player games. Such games are played along graphs in which each transition have a value in the lattice. The value of the game essentially denotes the truth value of the statement "the ∨-player can force the game to computations that satisfy the winning condition". An earlier definition of such games involved a zig-zagged traversal of paths generated during the game. Our definition involves a forward traversal of the paths, and it leads to better understanding of multi-valued games. In particular, we prove a min-max property for such games, and relate latticed simulation with latticed games.

Temporal logic query checking: a tool for model exploration

Temporal logic query checking was first introduced by W. Chan in order to speed up design understanding by discovering properties not known a priori. A query is a temporal logic formula containing a special symbol ?/sub 1/, known as a placeholder. Given a Kripke structure and a propositional formula /spl phi/, we say that /spl phi/ satisfies the query if replacing the placeholder by /spl phi/ results in a temporal logic formula satisfied by the Kripke structure. A solution to a temporal logic query on a Kripke structure is the set of all propositional formulas that satisfy the query. Query checking helps discover temporal properties of a system and, as such, is a useful tool for model exploration. In this paper, we show that query checking is applicable to a variety of model exploration tasks, ranging from invariant computation to test case generation. We illustrate these using a Cruise Control System. Additionally, we show that query checking is an instance of a multi-valued model checking of Chechik et al. This approach enables us to build an implementation of a temporal logic query checker, TLQSolver, on top of our existing multi-valued model checker /sub /spl chi//Chek. It also allows us to decide a large class of queries and introduce witnesses for temporal logic queries-an essential notion for effective model exploration.

Model exploration with temporal logic query checking

A temporal logic query is a temporal logic formula with placeholders. Given a model, a solution to a query is a set of assignments of propositional formulas to placeholders, such that replacing the placeholders with any of these assignments results in a temporal logic formula that holds in the model. Query checking, first introduced by William Chan [2], is an automated technique for finding solutions to temporal logic queries. It allows discovery of the temporal properties of the system and as such may be a useful tool for model exploration and reverse engineering.This paper describes an implementation of a temporal logic query checker. It then suggests some applications of this tool, ranging from invariant computation to test case generation, and illustrates them using a Cruise Control System.