Solving string constraints with Regex-dependent functions through transducers with priorities and variables

Regular expressions are a classical concept in formal language theory. Regular expressions in programming languages (RegEx) such as JavaScript, feature non-standard semantics of operators (e.g. greedy/lazy Kleene star), as well as additional features such as capturing groups and references. While symbolic execution of programs containing RegExes appeals to string solvers natively supporting important features of RegEx, such a string solver is hitherto missing. In this paper, we propose the first string theory and string solver that natively provides such support. The key idea of our string solver is to introduce a new automata model, called prioritized streaming string transducers (PSST), to formalize the semantics of RegEx-dependent string functions. PSSTs combine priorities, which have previously been introduced in prioritized finite-state automata to capture greedy/lazy semantics, with string variables as in streaming string transducers to model capturing groups. We validate the consistency of the formal semantics with the actual JavaScript semantics by extensive experiments. Furthermore, to solve the string constraints, we show that PSSTs enjoy nice closure and algorithmic properties, in particular, the regularity-preserving property (i.e., pre-images of regular constraints under PSSTs are regular), and introduce a sound sequent calculus that exploits these properties and performs propagation of regular constraints by means of taking post-images or pre-images. Although the satisfiability of the string constraint language is generally undecidable, we show that our approach is complete for the so-called straight-line fragment. We evaluate the performance of our string solver on over 195000 string constraints generated from an open-source RegEx library. The experimental results show the efficacy of our approach, drastically improving the existing methods (via symbolic execution) in both precision and efficiency.

Ontology-Based Transformation and Verification of UML/OCL Constraints

In Software Engineering (SE), the graphical models specify the system's architecture, connection, and characteristics. New SE methods such as MDA utilize graphical models as a nucleus of all development activities. This paper presents the transformation and verification of class diagram and Object Constraint Language (OCL) and transformation algorithm from Class model to ontology in the continuity of our research on UML and ontology integration. The class diagram is transformed into ontology, and constraints specified through OCL are transformed into SPARQL.

The Complexity of the Ideal Membership Problem for Constrained Problems Over the Boolean Domain

Given an ideal I and a polynomial f the Ideal Membership Problem (IMP) is to test if f ϵ I . This problem is a fundamental algorithmic problem with important applications and notoriously intractable. We study the complexity of the IMP for combinatorial ideals that arise from constrained problems over the Boolean domain. As our main result, we identify the borderline of tractability. By using Gröbner bases techniques, we extend Schaefer’s dichotomy theorem [STOC, 1978] which classifies all Constraint Satisfaction Problems (CSPs) over the Boolean domain to be either in P or NP-hard. Moreover, our result implies necessary and sufficient conditions for the efficient computation of Theta Body Semi-Definite Programming (SDP) relaxations, identifying therefore the borderline of tractability for constraint language problems. This article is motivated by the pursuit of understanding the recently raised issue of bit complexity of Sum-of-Squares (SoS) proofs [O’Donnell, ITCS, 2017]. Raghavendra and Weitz [ICALP, 2017] show how the IMP tractability for combinatorial ideals implies bounded coefficients in SoS proofs.

Formalizing Parameter Constraints to Support Intelligent Geoprocessing: A SHACL-Based Method

Intelligent geoprocessing relies heavily on formalized parameter constraints of geoprocessing tools to validate the input data and to further ensure the robustness and reliability of geoprocessing. However, existing methods developed to formalize parameter constraints are either designed based on ill-suited assumptions, which may not correctly identify the invalid parameter inputs situation, or are inefficient to use. This paper proposes a novel method to formalize the parameter constraints of geoprocessing tools, based on a high-level and standard constraint language (i.e., SHACL) and geoprocessing ontologies, under the guidance of a systematic classification of parameter constraints. An application case and a heuristic evaluation were conducted to demonstrate and evaluate the effectiveness and usability of the proposed method. The results show that the proposed method is not only comparatively easier and more efficient than existing methods but also covers more types of parameter constraints, for example, the application-context-matching constraints that have been ignored by existing methods.

Reasoning about Explanations for Non-validation in SHACL

The Shapes Constraint Language (SHACL) is a recently standardized language for describing and validating constraints over RDF graphs. The SHACL specification describes the so-called validation reports, which are meant to explain to the users the outcome of validating an RDF graph against a collection of constraints. Specifically, explaining the reasons why the input graph does not satisfy the constraints is challenging. In fact, the current SHACL standard leaves it open on how such explanations can be provided to the users. In this paper, inspired by works on logic-based abduction and database repairs, we study the problem of explaining non-validation of SHACL constraints. In particular, in our framework non-validation is explained using the notion of a repair, i.e., a collection of additions and deletions whose application on an input graph results in a repaired graph that does satisfy the given SHACL constraints. We define a collection of decision problems for reasoning about explanations, possibly restricting to explanations that are minimal with respect to cardinality or set inclusion. We provide a detailed characterization of the computational complexity of those reasoning tasks, including the combined and the data complexity.

Algebraic Approach to Promise Constraint Satisfaction

The complexity and approximability of the constraint satisfaction problem (CSP) has been actively studied over the past 20 years. A new version of the CSP, the promise CSP (PCSP), has recently been proposed, motivated by open questions about the approximability of variants of satisfiability and graph colouring. The PCSP significantly extends the standard decision CSP. The complexity of CSPs with a fixed constraint language on a finite domain has recently been fully classified, greatly guided by the algebraic approach, which uses polymorphisms—high-dimensional symmetries of solution spaces—to analyse the complexity of problems. The corresponding classification for PCSPs is wide open and includes some long-standing open questions, such as the complexity of approximate graph colouring, as special cases. The basic algebraic approach to PCSP was initiated by Brakensiek and Guruswami, and in this article, we significantly extend it and lift it from concrete properties of polymorphisms to their abstract properties. We introduce a new class of problems that can be viewed as algebraic versions of the (Gap) Label Cover problem and show that every PCSP with a fixed constraint language is equivalent to a problem of this form. This allows us to identify a “measure of symmetry” that is well suited for comparing and relating the complexity of different PCSPs via the algebraic approach. We demonstrate how our theory can be applied by giving both general and specific hardness/tractability results. Among other things, we improve the state-of-the-art in approximate graph colouring by showing that, for any k ≥ 3, it is NP-hard to find a (2 k -1)-colouring of a given k -colourable graph.

Automatic Detection of Metadata Errors in a Registry of Clinical Studies Using Shapes Constraint Language (SHACL) Graphs

Registries of clinical studies such as ClinicalTrials.gov are an important source of information. However, the process of manually entering metadata is prone to errors which impedes their use and thereby the overall usefulness of the registry. In this work, we propose a generic approach towards detection of errors in the metadata by using the Shapes Constraint Language for defining rule templates covering constraints regarding value type and cardinality. We developed a Python 3 algorithm for the automatic validation of 15 rule instances applied to the whole ClinicalTrials.gov database (355,862 studies; 27th October 2020) resulting in more than 5 million metadata verifications. Our results show a large number of errors in different metadata fields, such as i) missing values, ii) values not coming from a predefined set or iii) wrong cardinalities, can be detected using this approach. Since 2015 approximately 5% of all studies contain one or more errors. In the future, we will apply this technique to other registries and develop more complex rules by focusing on the semantics of the metadata. This could render the possibility of automatically correcting entries, increasing the value of registries of clinical studies.

Circuit Complexity Of Constraint Satisfaction Problems With Few Subpowers

Although Constraint Satisfaction Problems (CSPs) are generally known to be NP-complete, placing restrictions on the constraint template can yield tractable subclasses. By studying the operations in the polymorphism of the constraint language, we can construct algorithms which solve our CSP in polynomial time. Previous results for CSPs with Mal’tsev [7] and generalized majority-minority operations [10] were improved to include CSPs with k-edge operations [15]. We present an alternative method to solve k-edge CSPs by utilizing Boolean trees placing the problem in the class NC2 . We do this by arranging the logical formulas describing the CSP into a Boolean tree where each leaf represents a constraint in the CSP. We take the conjunction of the constraint formulas yielding partial solutions at every step until we are left with a solution set at the root of the tree which satisfies all of the constraints.

Circuit Complexity Of Constraint Satisfaction Problems With Few Subpowers

Although Constraint Satisfaction Problems (CSPs) are generally known to be NP-complete, placing restrictions on the constraint template can yield tractable subclasses. By studying the operations in the polymorphism of the constraint language, we can construct algorithms which solve our CSP in polynomial time. Previous results for CSPs with Mal’tsev [7] and generalized majority-minority operations [10] were improved to include CSPs with k-edge operations [15]. We present an alternative method to solve k-edge CSPs by utilizing Boolean trees placing the problem in the class NC2 . We do this by arranging the logical formulas describing the CSP into a Boolean tree where each leaf represents a constraint in the CSP. We take the conjunction of the constraint formulas yielding partial solutions at every step until we are left with a solution set at the root of the tree which satisfies all of the constraints.