Author name cluster

Mikolás Janota

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

20 papers

1 author row

ECAI Conference 2024 Conference Paper

Cube-Based Isomorph-Free Finite Model Finding

Choiwah Chow
Mikolás Janota
João Araújo 0002

Complete enumeration of finite models of first-order logic (FOL) formulas is pivotal to universal algebra, which studies and catalogs algebraic structures. Efficient finite model enumeration is highly challenging because the number of models grows rapidly with their size but at the same time, we are only interested in models modulo isomorphism. While isomorphism cuts down the number of models of interest, it is nontrivial to take that into account computationally. This paper develops a novel algorithm that achieves isomorphism-free enumeration by employing isomorphic graph detection algorithm nauty, cube-based search space splitting, and compact model representations. We name our algorithm cube-based isomorph-free finite model finding algorithm (CBIF). Our approach contrasts with the traditional two-step algorithms, which first enumerate (possibly isomorphic) models and then filter the isomorphic ones out in the second stage. The experimental results show that CBIF is many orders of magnitude faster than the traditional two-step algorithms. CBIF enables us to calculate new results that are not found in the literature, including the extension of two existing OEIS sequences, thereby advancing the state of the art.

LPAR Conference 2024 Conference Paper

First Experiments with Neural cvc5

Jelle Piepenbrock
Mikolás Janota
Josef Urban
Jan Jakubuv

The cvc5 solver is today one of the strongest systems for solving first order problems with theories but also without them. In this work we equip its enumeration-based instan- tiation with a neural network that guides the choice of the quantified formulas and their instances. For that we develop a relatively fast graph neural network that repeatedly scores all available instantiation options with respect to the available formulas. The network runs directly on a CPU without the need for any special hardware. We train the neural guidance on a large set of proofs generated by the e-matching instantiation strategy and evaluate its performance on a set of previously unseen problems.

ECAI Conference 2024 Conference Paper

Machine Learning for Quantifier Selection in cvc5

Jan Jakubuv
Mikolás Janota
Jelle Piepenbrock
Josef Urban

In this work we considerably improve the state-of-the-art SMT solving on first-order quantified problems by efficient machine learning guidance of quantifier selection. Quantifiers represent a significant challenge for SMT and are technically a source of undecidability. In our approach, we train an efficient machine learning model that informs the solver which quantifiers should be instantiated and which not. Each quantifier may be instantiated multiple times and the set of the active quantifiers changes as the solving progresses. Therefore, we invoke the ML predictor many times, during the whole run of the solver. To make this efficient, we use fast ML models based on gradient boosted decision trees. We integrate our approach into the state-of-the-art cvc5 SMT solver and show a considerable increase of the system’s holdout-set performance after training it on a large set of first-order problems collected from the Mizar Mathematical Library.

LPAR Conference 2023 Conference Paper

A Mathematical Benchmark for Inductive Theorem Provers

Thibault Gauthier
Chad E. Brown
Mikolás Janota
Josef Urban

We present a benchmark of 29687 problems derived from the On-Line Encyclopedia of Integer Sequences (OEIS). Each problem expresses the equivalence of two syntactically different programs generating the same OEIS sequence. Such programs were conjectured by a learning-guided synthesis system using a language with looping operators. The operators implement recursion, and thus many of the proofs require induction on natural numbers. The benchmark contains problems of varying difficulty from a wide area of mathematical domains. We believe that these characteristics will make it an effective judge for the progress of inductive theorem provers in this domain for years to come.

LPAR Conference 2023 Conference Paper

Experiments on Infinite Model Finding in SMT Solving

Julian Parsert
Chad E. Brown
Mikolás Janota
Cezary Kaliszyk

We propose infinite model finding as a new task for SMT-Solving. Model finding has a long-standing tradition in SMT and automated reasoning in general. Yet, most of the current tools are limited to finite models despite the fact that many theories only admit infinite models. This paper shows a variety of such problems and evaluates synthesis approaches on them. Interestingly, state-of-the-art SMT solvers fail even on very small and simple problems. We target such problems by SyGuS tools as well as heuristic approaches.

ECAI Conference 2023 Conference Paper

Graph Neural Networks for Mapping Variables Between Programs

Pedro Orvalho
Jelle Piepenbrock
Mikolás Janota
Vasco Manquinho

Automated program analysis is a pivotal research domain in many areas of Computer Science — Formal Methods and Artificial Intelligence, in particular. Due to the undecidability of the problem of program equivalence, comparing two programs is highly challenging. Typically, in order to compare two programs, a relation between both programs’ sets of variables is required. Thus, mapping variables between two programs is useful for a panoply of tasks such as program equivalence, program analysis, program repair, and clone detection. In this work, we propose using graph neural networks (GNNs) to map the set of variables between two programs based on both programs’ abstract syntax trees (ASTs). To demonstrate the strength of variable mappings, we present three use-cases of these mappings on the task of program repair to fix well-studied and recurrent bugs among novice programmers in introductory programming assignments (IPAs). Experimental results on a dataset of 4166 pairs of incorrect/correct programs show that our approach correctly maps 83% of the evaluation dataset. Moreover, our experiments show that the current state-of-the-art on program repair, greatly dependent on the programs’ structure, can only repair about 72% of the incorrect programs. In contrast, our approach, which is solely based on variable mappings, can repair around 88. 5%.

SAT Conference 2022 Conference Paper

SAT-Based Leximax Optimisation Algorithms

Miguel Cabral
Mikolás Janota
Vasco Manquinho

In several real-world problems, it is often the case that the goal is to optimise several objective functions. However, usually there is not a single optimal objective vector. Instead, there are many optimal objective vectors known as Pareto-optima. Finding all Pareto-optima is computationally expensive and the number of Pareto-optima can be too large for a user to analyse. A compromise can be made by defining an optimisation criterion that integrates all objective functions. In this paper we propose several SAT-based algorithms to solve multi-objective optimisation problems using the leximax criterion. The leximax criterion is used to obtain a Pareto-optimal solution with a small trade-off between the objective functions, which is suitable in problems where there is an absence of priorities between the objective functions. Experimental results on the Multi-Objective Package Upgradeability Optimisation problem show that the SAT-based algorithms are able to outperform the Integer Linear Programming (ILP) approach when using non-commercial ILP solvers. Additionally, experimental results on selected instances from the MaxSAT evaluation adapted to the multi-objective domain show that our approach outperforms the ILP approach using commercial solvers.

SAT Conference 2022 Conference Paper

Towards Learning Quantifier Instantiation in SMT

Mikolás Janota
Jelle Piepenbrock
Bartosz Piotrowski

This paper applies machine learning (ML) to solve quantified satisfiability modulo theories (SMT) problems more efficiently. The motivating idea is that the solver should learn from already solved formulas to solve new ones. This is especially relevant in classes of similar formulas. We focus on the enumerative instantiation - a well-established approach to solving quantified formulas anchored in the Herbrand’s theorem. The task is to select the right ground terms to be instantiated. In ML parlance, this means learning to rank ground terms. We devise a series of features of the considered terms and train on them using boosted decision trees. In particular, we integrate the LightGBM library into the SMT solver cvc5. The experimental results demonstrate that the ML-guided solver enables us to solve more formulas than the base solver and reduce the number of quantifier instantiations. We also do an ablation study on the features used in the machine learning component, showing the contributions of the various additions.

SAT Conference 2020 Conference Paper

SAT-Based Encodings for Optimal Decision Trees with Explicit Paths

Mikolás Janota
António Morgado 0001

Abstract Decision trees play an important role both in Machine Learning and Knowledge Representation. They are attractive due to their immediate interpretability. In the spirit of Occam’s razor, and interpretability, it is desirable to calculate the smallest tree. This, however, has proven to be a challenging task and greedy approaches are typically used to learn trees in practice. Nevertheless, recent work showed that by the use of SAT solvers one may calculate the optimal size tree for real-world benchmarks. This paper proposes a novel SAT-based encoding that explicitly models paths in the tree, which enables us to control the tree’s depth as well as size. At the level of individual SAT calls, we investigate splitting the search space into tree topologies. Our tool outperforms the existing implementation. But also, the experimental results show that minimizing the depth first and then minimizing the number of nodes enables solving a larger set of instances.

SAT Conference 2018 Conference Paper

Circuit-Based Search Space Pruning in QBF

Mikolás Janota

Abstract This paper describes the algorithm implemented in the QBF solver CQESTO, which has placed second in the non-CNF track of the last year’s QBF competition. The algorithm is inspired by the CNF-based solver QESTO. Just as QESTO, CQESTO invokes a SAT solver in a black-box fashion. However, it directly operates on the circuit representation of the formula. The paper analyzes the individual operations that the solver performs.

LPAR Conference 2018 Conference Paper

Towards Smarter MACE-style Model Finders

Mikolás Janota
Martin Suda 0001

Finite model finders represent a powerful tool for deciding problems with the finite model property, such as the Bernays-Sch ̈onfinkel fragment (EPR). Further, finite model finders provide useful information for counter-satisfiable conjectures. The paper investigates several novel techniques in a finite model-finder based on the translation to SAT, referred to as the MACE-style approach. The approach we propose is driven by counterexample abstraction refinement (CEGAR), which has proven to be a powerful tool in the context of quantifiers in satisfiability modulo theories (SMT) and quantified Boolean formulas (QBF). One weakness of CEGAR-based approaches is that certain amount of luck is required in order to guess the right model, because the solver always operates on incomplete information about the formula. To tackle this issue, we propose to enhance the model finder with a machine learning algorithm to improve the likelihood that the right model is encountered. The implemented prototype based on the presented ideas shows highly promising results.

SAT Conference 2016 Conference Paper

On Q-Resolution and CDCL QBF Solving

Mikolás Janota

Abstract The proof system Q-resolution and its variations provide the underlying proof systems for the DPLL-based QBF solvers. While (long-distance) Q-resolution models a conflict driven clause learning (CDCL) QBF solver, the inverse relation is not well understood. This paper shows that CDCL solving not only does not simulate Q-resolution, but also that this is deeply embedded in the workings of the solver. This contrasts with SAT solving, where CDCL solvers have been shown to simulate resolution.

SAT Conference 2015 Conference Paper

Exploiting Resolution-Based Representations for MaxSAT Solving

Miguel Terra-Neves
Ruben Martins
Mikolás Janota
Inês Lynce
Vasco Manquinho

Abstract Most recent MaxSAT algorithms rely on a succession of calls to a SAT solver in order to find an optimal solution. In particular, several algorithms take advantage of the ability of SAT solvers to identify unsatisfiable subformulas. Usually, these MaxSAT algorithms perform better when small unsatisfiable subformulas are found in early iterations of the algorithm. However, this is not the case in many problem instances, since the whole formula is given to the SAT solver in each call. In this paper, we propose to partition the MaxSAT formula using a resolution-based graph representation. Partitions are then iteratively joined by using a proximity measure extracted from the graph representation of the formula. The algorithm ends when only one partition remains and the optimal solution is found. Experimental results show that this new approach further enhances a state of the art MaxSAT solver to optimally solve a larger set of industrial problem instances.

SAT Conference 2013 Conference Paper

On Propositional QBF Expansions and Q-Resolution

Mikolás Janota
João Marques-Silva 0001

Abstract Over the years, proof systems for propositional satisfiability (SAT) have been extensively studied. Recently, proof systems for quantified Boolean formulas (QBFs) have also been gaining attention. Q-resolution is a calculus enabling producing proofs from DPLL-based QBF solvers. While DPLL has become a dominating technique for SAT, QBF has been tackled by other complementary and competitive approaches. One of these approaches is based on expanding variables until the formula contains only one type of quantifier; upon which a SAT solver is invoked. This approach motivates the theoretical analysis carried out in this paper. We focus on a two phase proof system, which expands the formula in the first phase and applies propositional resolution in the second. Fragments of this proof system are defined and compared to Q-resolution.

LPAR Conference 2013 Conference Paper

On QBF Proofs and Preprocessing

Mikolás Janota
Radu Grigore
João Marques-Silva 0001

Abstract QBFs (quantified boolean formulas), which are a superset of propositional formulas, provide a canonical representation for PSPACE problems. To overcome the inherent complexity of QBF, significant effort has been invested in developing QBF solvers as well as the underlying proof systems. At the same time, formula preprocessing is crucial for the application of QBF solvers. This paper focuses on a missing link in currently-available technology: How to obtain a certificate (e. g. proof) for a formula that had been preprocessed before it was given to a solver? The paper targets a suite of commonly-used preprocessing techniques and shows how to reconstruct certificates for them. On the negative side, the paper discusses certain limitations of the currently-used proof systems in the light of preprocessing. The presented techniques were implemented and evaluated in the state-of-the-art QBF preprocessor bloqqer.

SAT Conference 2013 Conference Paper

Quantified Maximum Satisfiability: - A Core-Guided Approach

Alexey Ignatiev
Mikolás Janota
João Marques-Silva 0001

Abstract In recent years, there have been significant improvements in algorithms both for Quantified Boolean Formulas (QBF) and for Maximum Satisfiability (MaxSAT). This paper studies the problem of solving quantified formulas subject to a cost function, and considers the problem in a quantified MaxSAT setting. Two approaches are investigated. One is based on relaxing the soft clauses and performing a linear search on the cost function. The other approach, which is the main contribution of the paper, is inspired by recent work on MaxSAT, and exploits the iterative identification of unsatisfiable cores. The paper investigates the application of these approaches to the concrete problem of computing smallest minimal unsatisfiable subformulas (SMUS), a decision version of which is a well-known problem in the second level of the polynomial hierarchy. Experimental results, obtained on representative problem instances, indicate that the core-guided approach for the SMUS problem outperforms the use of linear search over the values of the cost function. More significantly, the core-guided approach also outperforms the state-of-the-art SMUS extractor Digger.

SAT Conference 2012 Conference Paper

Solving QBF with Counterexample Guided Refinement

Mikolás Janota
William Klieber
João Marques-Silva 0001
Edmund M. Clarke

Abstract We propose two novel approaches for using Counterexample-Guided Abstraction Refinement (CEGAR) in Quantified Boolean Formula (QBF) solvers. The first approach develops a recursive algorithm whose search is driven by CEGAR (rather than by DPLL). The second approach employs CEGAR as an additional learning technique in an existing DPLL-based QBF solver. Experimental evaluation of the implemented prototypes shows that the CEGAR-driven solver outperforms existing solvers on a number of families in the QBF-LIB and that the DPLL solver benefits from the additional type of learning. Thus this article opens two promising avenues in QBF: CEGAR-driven solvers as an alternative to existing approaches and a novel type of learning in DPLL.

SAT Conference 2011 Conference Paper

Abstraction-Based Algorithm for 2QBF

Mikolás Janota
João Marques-Silva 0001

Abstract Quantified Boolean Formulas (QBFs) enable standard representation of PSPACE problems. In particular, formulas with two quantifier levels (2QBFs) enable representing problems in the second level of the polynomial hierarchy (Π 2 P, Σ 2 P ). This paper proposes an algorithm for solving 2QBF satisfiability by counterexample guided abstraction refinement (CEGAR). This represents an alternative approach to 2QBF satisfiability and, by extension, to solving decision problems in the second level of polynomial hierarchy. In addition, the paper presents a comparison of a prototype implementing the presented algorithm to state of the art QBF solvers, showing that a larger set of instances is solved.

JELIA Conference 2010 Conference Paper

Counterexample Guided Abstraction Refinement Algorithm for Propositional Circumscription

Mikolás Janota
Radu Grigore
João Marques-Silva 0001

Abstract Circumscription is a representative example of a nonmonotonic reasoning inference technique. Circumscription has often been studied for first order theories, but its propositional version has also been the subject of extensive research, having been shown equivalent to extended closed world assumption (ECWA). Moreover, entailment in propositional circumscription is a well-known example of a decision problem in the second level of the polynomial hierarchy. This paper proposes a new Boolean Satisfiability (SAT)-based algorithm for entailment in propositional circumscription that explores the relationship of propositional circumscription to minimal models. The new algorithm is inspired by ideas commonly used in SAT-based model checking, namely counterexample guided abstraction refinement. In addition, the new algorithm is refined to compute the theory closure for generalized close world assumption (GCWA). Experimental results show that the new algorithm can solve problem instances that other solutions are unable to solve.

ECAI Conference 2010 Conference Paper

On Computing Backbones of Propositional Theories

João Marques-Silva 0001
Mikolás Janota
Inês Lynce

Backbones of propositional theories are literals that are true in every model. Backbones have been used for characterizing the hardness of decision and optimization problems. Moreover, backbones find other applications. For example, backbones are often identified during product configuration. Backbones can also improve the efficiency of solving computational problems related with propositional theories. These include model enumeration, minimal model computation and prime implicant computation. This paper investigates algorithms for computing backbones of propositional theories, emphasizing the integration of these algorithms with modern SAT solvers. Experimental results, obtained on representative problem instances, indicate that the proposed algorithms are effective in practice and can be used for computing the backbones of large propositional theories. In addition, the experimental results indicate that propositional theories can have large backbones, often representing a significant percentage of the total number of variables.