arXiv subjects

Moshe Vardi

Publications and source records attributed to Moshe Vardi.

13 recordsLinked to original sources

arXiv2026

Categorizer Automata for Discounted-Sum Payoffs

Categorizing continuous data into discrete bins is a fundamental operation in artificial intelligence. We introduce the categorizer automaton, a deterministic automaton that reads an infinite sequence of rewards and identifies which of finitely many bins contains its discounted sum. Categorizer automata generalize comparator automata, the special case of two bins, which have already proven useful in quantitative synthesis. Our main technical contribution is the construction of a categorizer automaton whose state space is linear in the number of bins, rather than exponential as obtained by a cross-product of comparator automata. We then apply categorizer automata to Markov decision processes, where they allow one to synthesize policies that maximize the expected utility of a discounted-sum payoff for utility functions that may be discontinuous. For piecewise-constant utility functions, the resulting algorithm is exact and runs in pseudo-polynomial time. For piecewise-Lipschitz utility functions, a class that includes any utility with bounded slope between finitely many jumps, it again runs in pseudo-polynomial time and yields an $\varepsilon$-optimal policy. We also show that the synthesis problem considered is PSPACE-hard already for piecewise-constant utilities.

cs.AI↗

arXiv2024

The Trembling-Hand Problem for LTLf Planning

Consider an agent acting to achieve its temporal goal, but with a "trembling hand". In this case, the agent may mistakenly instruct, with a certain (typically small) probability, actions that are not intended due to faults or imprecision in its action selection mechanism, thereby leading to possible goal failure. We study the trembling-hand problem in the context of reasoning about actions and planning for temporally extended goals expressed in Linear Temporal Logic on finite traces (LTLf), where we want to synthesize a strategy (aka plan) that maximizes the probability of satisfying the LTLf goal in spite of the trembling hand. We consider both deterministic and nondeterministic (adversarial) domains. We propose solution techniques for both cases by relying respectively on Markov Decision Processes and on Markov Decision Processes with Set-valued Transitions with LTLf objectives, where the set-valued probabilistic transitions capture both the nondeterminism from the environment and the possible action instruction errors from the agent. We formally show the correctness of our solution techniques and demonstrate their effectiveness experimentally through a proof-of-concept implementation.

cs.RO↗

arXiv2021

Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective

Neural-symbolic computing has now become the subject of interest of both academic and industry research laboratories. Graph Neural Networks (GNN) have been widely used in relational and symbolic domains, with widespread application of GNNs in combinatorial optimization, constraint satisfaction, relational reasoning and other scientific domains. The need for improved explainability, interpretability and trust of AI systems in general demands principled methodologies, as suggested by neural-symbolic computing. In this paper, we review the state-of-the-art on the use of GNNs as a model of neural-symbolic computing. This includes the application of GNNs in several domains as well as its relationship to current developments in neural-symbolic computing.

cs.AI↗

arXiv2020

Computer-Aided Personalized Education

The shortage of people trained in STEM fields is becoming acute, and universities and colleges are straining to satisfy this demand. In the case of computer science, for instance, the number of US students taking introductory courses has grown three-fold in the past decade. Recently, massive open online courses (MOOCs) have been promoted as a way to ease this strain. This at best provides access to education. The bigger challenge though is coping with heterogeneous backgrounds of different students, retention, providing feedback, and assessment. Personalized education relying on computational tools can address this challenge. While automated tutoring has been studied at different times in different communities, recent advances in computing and education technology offer exciting opportunities to transform the manner in which students learn. In particular, at least three trends are significant. First, progress in logical reasoning, data analytics, and natural language processing has led to tutoring tools for automatic assessment, personalized instruction including targeted feedback, and adaptive content generation for a variety of subjects. Second, research in the science of learning and human-computer interaction is leading to a better understanding of how different students learn, when and what types of interventions are effective for different instructional goals, and how to measure the success of educational tools. Finally, the recent emergence of online education platforms, both in academia and industry, is leading to new opportunities for the development of a shared infrastructure. This CCC workshop brought together researchers developing educational tools based on technologies such as logical reasoning and machine learning with researchers in education, human-computer interaction, and cognitive psychology.

cs.CY↗

arXiv2020

Strategy Logic with Imperfect Information

We introduce an extension of Strategy Logic for the imperfect-information setting, called SLii, and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, this problem is undecidable; but we introduce a syntactical class of "hierarchical instances" for which, intuitively, as one goes down the syntactic tree of the formula, strategy quantifications are concerned with finer observations of the model, and we prove that model-checking SLii restricted to hierarchical instances is decidable. To establish this result we go through QCTL, an intermediary, "low-level" logic much more adapted to automata techniques. QCTL is an extension of CTL with second-order quantification over atomic propositions. We extend it to the imperfect information setting by parameterising second-order quantifiers with observations. While the model-checking problem of QCTLii is, in general, undecidable, we identify a syntactic fragment of hierarchical formulas and prove, using an automata-theoretic approach, that it is decidable. We apply our result to solve complex strategic problems in the imperfect-information setting. We first show that the existence of Nash equilibria for deterministic strategies is decidable in games with hierarchical information. We also introduce distributed rational synthesis, a generalisation of rational synthesis to the imperfect-information setting. Because it can easily be expressed in our logic, our main result provides solution to this problem in the case of hierarchical information.

cs.LO↗

arXiv2019

LTLf Synthesis with Fairness and Stability Assumptions

In synthesis, assumptions are constraints on the environment that rule out certain environment behaviors. A key observation here is that even if we consider systems with LTLf goals on finite traces, environment assumptions need to be expressed over infinite traces, since accomplishing the agent goals may require an unbounded number of environment action. To solve synthesis with respect to finite-trace LTLf goals under infinite-trace assumptions, we could reduce the problem to LTL synthesis. Unfortunately, while synthesis in LTLf and in LTL have the same worst-case complexity (both 2EXPTIME-complete), the algorithms available for LTL synthesis are much more difficult in practice than those for LTLf synthesis. In this work we show that in interesting cases we can avoid such a detour to LTL synthesis and keep the simplicity of LTLf synthesis. Specifically, we develop a BDD-based fixpoint-based technique for handling basic forms of fairness and of stability assumptions. We show, empirically, that this technique performs much better than standard LTL synthesis.

cs.AI↗

arXiv2018

Learning to Solve NP-Complete Problems - A Graph Neural Network for Decision TSP

Graph Neural Networks (GNN) are a promising technique for bridging differential programming and combinatorial domains. GNNs employ trainable modules which can be assembled in different configurations that reflect the relational structure of each problem instance. In this paper, we show that GNNs can learn to solve, with very little supervision, the decision variant of the Traveling Salesperson Problem (TSP), a highly relevant $\mathcal{NP}$-Complete problem. Our model is trained to function as an effective message-passing algorithm in which edges (embedded with their weights) communicate with vertices for a number of iterations after which the model is asked to decide whether a route with cost $<C$ exists. We show that such a network can be trained with sets of dual examples: given the optimal tour cost $C^{*}$, we produce one decision instance with target cost $x\%$ smaller and one with target cost $x\%$ larger than $C^{*}$. We were able to obtain $80\%$ accuracy training with $-2\%,+2\%$ deviations, and the same trained model can generalize for more relaxed deviations with increasing performance. We also show that the model is capable of generalizing for larger problem sizes. Finally, we provide a method for predicting the optimal route cost within $2\%$ deviation from the ground truth. In summary, our work shows that Graph Neural Networks are powerful enough to solve $\mathcal{NP}$-Complete problems which combine symbolic and numeric data.

cs.LG↗

arXiv2018

Strategy Logic with Imperfect Information

We introduce an extension of Strategy Logic for the imperfect-information setting, called SLii, and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, the problem turns out to be undecidable. We introduce a syntactical class of "hierarchical instances" for which, intuitively, as one goes down the syntactic tree of the formula, strategy quantifications are concerned with finer observations of the model. We prove that model-checking SLii restricted to hierarchical instances is decidable. This result, because it allows for complex patterns of existential and universal quantification on strategies, greatly generalises previous ones, such as decidability of multi-player games with imperfect information and hierarchical observations, and decidability of distributed synthesis for hierarchical systems. To establish the decidability result, we introduce and study QCTL*ii, an extension of QCTL* (itself an extension of CTL* with second-order quantification over atomic propositions) by parameterising its quantifiers with observations. The simple syntax of QCTL* ii allows us to provide a conceptually neat reduction of SLii to QCTL*ii that separates concerns, allowing one to forget about strategies and players and focus solely on second-order quantification. While the model-checking problem of QCTL*ii is, in general, undecidable, we identify a syntactic fragment of hierarchical formulas and prove, using an automata-theoretic approach, that it is decidable. The decidability result for SLii follows since the reduction maps hierarchical instances of SLii to hierarchical formulas of QCTL*ii .

cs.LO↗

arXiv2017

Safety Model Checking with Complementary Approximations

Formal verification techniques such as model checking, are becoming popular in hardware design. SAT-based model checking techniques such as IC3/PDR, have gained a significant success in hardware industry. In this paper, we present a new framework for SAT-based safety model checking, named Complementary Approximate Reachability (CAR). CAR is based on standard reachability analysis, but instead of maintaining a single sequence of reachable- state sets, CAR maintains two sequences of over- and under- approximate reachable-state sets, checking safety and unsafety at the same time. To construct the two sequences, CAR uses standard Boolean-reasoning algorithms, based on satisfiability solving, one to find a satisfying cube of a satisfiable Boolean formula, and one to provide a minimal unsatisfiable core of an unsatisfiable Boolean formula. We applied CAR to 548 hardware model-checking instances, and compared its performance with IC3/PDR. Our results show that CAR is able to solve 42 instances that cannot be solved by IC3/PDR. When evaluated against a portfolio that includes IC3/PDR and other approaches, CAR is able to solve 21 instances that the other approaches cannot solve. We conclude that CAR should be considered as a valuable member of any algorithmic portfolio for safety model checking.

cs.LO↗

arXiv2015

Constrained Sampling and Counting: Universal Hashing Meets SAT Solving

Constrained sampling and counting are two fundamental problems in artificial intelligence with a diverse range of applications, spanning probabilistic reasoning and planning to constrained-random verification. While the theory of these problems was thoroughly investigated in the 1980s, prior work either did not scale to industrial size instances or gave up correctness guarantees to achieve scalability. Recently, we proposed a novel approach that combines universal hashing and SAT solving and scales to formulas with hundreds of thousands of variables without giving up correctness guarantees. This paper provides an overview of the key ingredients of the approach and discusses challenges that need to be overcome to handle larger real-world instances.

cs.AI↗

arXiv2015

SAT-based Explicit LTL Reasoning

We present here a new explicit reasoning framework for linear temporal logic (LTL), which is built on top of propositional satisfiability (SAT) solving. As a proof-of-concept of this framework, we describe a new LTL satisfiability tool, Aalta\_v2.0, which is built on top of the MiniSAT SAT solver. We test the effectiveness of this approach by demonnstrating that Aalta\_v2.0 significantly outperforms all existing LTL satisfiability solvers. Furthermore, we show that the framework can be extended from propositional LTL to assertional LTL (where we allow theory atoms), by replacing MiniSAT with the Z3 SMT solver, and demonstrating that this can yield an exponential improvement in performance.

cs.LO↗

arXiv2015

Mode-Target Games: Reactive Synthesis for Control Applications

In this paper we introduce a class of Linear Temporal Logic (LTL) specifications for which the problem of synthesizing controllers can be solved in polynomial time. The new class of specifications is an LTL fragment that we term Mode-Target (MT) and is inspired by numerous control applications where there are modes and corresponding (possibly multiple) targets for each mode. We formulate the problem of synthesizing a controller enforcing an MT specification as a game and provide an algorithm that requires $O(\sum_i t_i n^2)$ symbolic steps, where $n$ is the number of states in the game graph, and $t_i$ is the number of targets corresponding to mode $i$.

math.OC↗

arXiv2011

Synthesis from Recursive-Components Libraries

Synthesis is the automatic construction of a system from its specification. In classical synthesis algorithms it is always assumed that the system is "constructed from scratch" rather than composed from reusable components. This, of course, rarely happens in real life. In real life, almost every non-trivial commercial software system relies heavily on using libraries of reusable components. Furthermore, other contexts, such as web-service orchestration, can be modeled as synthesis of a system from a library of components. In 2009 we introduced LTL synthesis from libraries of reusable components. Here, we extend the work and study synthesis from component libraries with "call and return"' control flow structure. Such control-flow structure is very common in software systems. We define the problem of Nested-Words Temporal Logic (NWTL) synthesis from recursive component libraries, where NWTL is a specification formalism, richer than LTL, that is suitable for "call and return" computations. We solve the problem, providing a synthesis algorithm, and show the problem is 2EXPTIME-complete, as standard synthesis.

cs.LO↗