# Moshe VardiRice University · Department of Computer Science

Moshe Vardi

PhD

## About

882

Publications

145,557

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39,903

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Introduction

Interested in Logic and Computation, see
http://www.cs.rice.edu/~vardi

Additional affiliations

December 1993 - December 2012

August 1985 - August 1995

**IBM Almaden Research Center, San Jose**

Position

- Research Staff Member and Department Manager

## Publications

Publications (882)

Task planning is the problem of finding a discrete sequence of actions to achieve a goal. Unfortunately, task planning in robotic domains is computationally challenging. To address this, in our prior work, we explained how knowledge from a successful task solution can be cached for later use, as an "abstract skill." Such a skill is represented as a...

The notion of comparison between system runs is fundamental in formal verification. This concept is implicitly present in the verification of qualitative systems, and is more pronounced in the verification of quantitative systems. In this work, we identify a novel mode of comparison in quantitative systems: the online comparison of the aggregate va...

Synthesis techniques for temporal logic specifications are typically based on exploiting symbolic techniques, as done in model checking. These symbolic techniques typically use backward fixpoint computation. Planning, which can be seen as a specific form of synthesis, is a witness of the success of forward search approaches. In this paper, we devel...

The problem of exact weighted sampling of solutions of Boolean formulas has applications in Bayesian inference, testing, and verification. The state-of-the-art approach to sampling involves carefully decomposing the input formula and compiling a data structure called d-DNNF in the process. Recent work in the closely connected field of model countin...

The problems of verification and realizability are two central themes in the analysis of reactive systems. When multiagent systems are considered, these problems have natural analogues of existence (nonemptiness) of pure-strategy Nash equilibria and verification of pure-strategy Nash equilibria. Recently, this body of work has begun to include fini...

Do agents know each others’ strategies? In multi-process software construction, each process has access to the processes already constructed; but in typical human-robot interactions, a human may not announce its strategy to the robot (indeed, the human may not even know their own strategy). This question has often been overlooked when modeling and...

Reactive synthesis from high-level specifications that combine hard constraints expressed in Linear Temporal Logic (LTL) with soft constraints expressed by discounted sum (DS) rewards has applications in planning and reinforcement learning. An existing approach combines techniques from LTL synthesis with optimization for the DS rewards but has fail...

The need to understand the inner workings of opaque Machine Learning models has prompted researchers to devise various types of post-hoc explanations. A large class of such explainers proceed in two phases: first perturb an input instance whose explanation is sought, and then generate an interpretable artifact to explain the prediction of the opaqu...

The determinization of a nondeterministic B\"uchi automaton (NBA) is a fundamental construction of automata theory, with applications to probabilistic verification and reactive synthesis. The standard determinization constructions, such as the ones based on the Safra-Piterman's approach, work on the whole NBA. In this work we propose a divide-and-c...

Solving realistic robotic task planning problems is computationally demanding. To better exploit the planning effort, and reduce the future planning cost, it is important to increase the reusability of successful plans. To this end, we suggest a systematic and automatable approach for plan transfer, by rethinking the plan caching procedure. Specifi...

Reactive synthesis from high-level specifications that combine hard constraints expressed in Linear Temporal Logic LTL with soft constraints expressed by discounted-sum (DS) rewards has applications in planning and reinforcement learning. An existing approach combines techniques from LTL synthesis with optimization for the DS rewards but has failed...

In Bayesian inference, the maximum a posteriori (MAP) problem combines the most probable explanation (MPE) and marginalization (MAR) problems. The counterpart in propositional logic is the exist-random stochastic satisfiability (ER-SSAT) problem, which combines the satisfiability (SAT) and weighted model counting (WMC) problems. Both MAP and ER-SSA...

In Bayesian inference, the most probable explanation (MPE) problem requests a variable instantiation with the highest probability given some evidence. Since a Bayesian network can be encoded as a literal-weighted CNF formula $\varphi$, we study Boolean MPE, a more general problem that requests a model $\tau$ of $\varphi$ with the highest weight, wh...

Boolean MaxSAT, as well as generalized formulations such as Min-MaxSAT and Max-hybrid-SAT, are fundamental optimization problems in Boolean reasoning. Existing methods for MaxSAT have been successful in solving benchmarks in CNF format. They lack, however, the ability to handle hybrid and generalized MaxSAT problems natively. To address this issue,...

The problems of \emph{verification} and \emph{realizability} are two central themes in the analysis of reactive systems. When multiagent systems are considered, these problems have natural analogues of existence (nonemptiness) of pure-strategy Nash equilibria and verification of pure-strategy Nash equilibria. Recently, this body of work has begun t...

Mission-time Linear Temporal Logic (LTL), abbreviated as MLTL, is a bounded variant of Metric Temporal Logic (MTL) over naturals designed to generically specify requirements for mission-based system operation common to aircraft, spacecraft, vehicles, and robots. Despite the utility of MLTL as a specification logic, major gaps remain in analyzing ML...

The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple and natural formalization of sequential decomposition, in which a task is decomposed into two sequential sub-...

Why was the world not ready for COVID-19, in spite of many warnings over the past 20 years of the high likelihood of a global pandemic? This chapter argues that the economic goal of efficiency, focused on short-term optimization, has distracted us from resilience, which is focused on long-term optimization. Computing also seems to have generally em...

Motivated by applications in boolean-circuit design, boolean synthesis is the process of synthesizing a boolean function with multiple outputs, given a relation between its inputs and outputs. Previous work has attempted to solve boolean functional synthesis by converting a specification formula into a Binary Decision Diagram (BDD) and quantifying...

The determinization of a nondeterministic Büchi automaton (NBA) is a fundamental construction of automata theory, with applications to probabilistic verification and reactive synthesis. The standard determinization constructions, such as the ones based on the Safra-Piterman’s approach, work on the whole NBA. In this work we propose a divide-and-con...

We revisit congruence relations for Büchi automata, which play a central role in automata-based formal verification. The size of the classical congruence relation is in 3O(n2), where n is the number of states of the given Büchi automaton. We present improved congruence relations that can be exponentially coarser than the classical one. We further g...

Linear Temporal Logic (LTL), proposed by Pnueli in 1977 for reasoning about ongoing programs, was defined over infinite traces. The motivation for this was the desire to model arbitrarily long computations. While this approach has been highly successful in the context of model checking, it has been less successful in the context of reactive synthes...

In this work, we exploit the power of \emph{finite ambiguity} for the complementation problem of B\"uchi automata by using reduced run directed acyclic graphs (DAGs) over infinite words, in which each vertex has at most one predecessor; these reduced run DAGs have only a finite number of infinite runs, thus obtaining the finite ambiguity in B\"uchi...

Temporal logics are widely used by the Formal Methods and AI communities. Linear Temporal Logic is a popular temporal logic and is valued for its ease of use as well as its balance between expressiveness and complexity. LTL is equivalent in expressiveness to Monadic First-Order Logic and satisfiability for LTL is PSPACE-complete. Linear Dynamic Log...

We consider the problem of synthesizing good-enough (GE)-strategies for linear temporal logic (LTL) over finite traces or LTLf for short. The problem of synthesizing GE-strategies for an LTL formula φ over infinite traces reduces to the problem of synthesizing winning strategies for the formula (∃Oφ)⇒φ where O is the set of propositions controlled...

In the Adapter Design Pattern , a programmer implements a Target interface by constructing an Adapter that accesses an existing Adaptee code. In this work, we present a reactive synthesis interpretation to the adapter design pattern, wherein an algorithm takes an Adaptee and a Target transducers, and the aim is to synthesize an Adapter transducer t...

Recent work in weighted model counting proposed a unifying framework for dynamic-programming algorithms. The core of this framework is a project-join tree: an execution plan that specifies how Boolean variables are eliminated. We adapt this framework to compute exact literal-weighted projected model counts of propositional formulas in conjunctive n...

The Boolean SATisfiability problem (SAT) is of central importance in computer science. Although SAT is known to be NP-complete, progress on the engineering side—especially that of Conflict-Driven Clause Learning (CDCL) and Local Search SAT solvers—has been remarkable. Yet, while SAT solvers, aimed at solving industrial-scale benchmarks in Conjuncti...

In the \emph{Adapter Design Pattern}, a programmer implements a \emph{Target} interface by constructing an \emph{Adapter} that accesses an existing \emph{Adaptee} code. In this work, we present a reactive synthesis interpretation to the adapter design pattern, wherein an algorithm takes an \emph{Adaptee} and a \emph{Target} transducers, and the aim...

Linear Temporal Logic (LTL) synthesis aims at automatically synthesizing a program that complies with desired properties expressed in LTL. Unfortunately it has been proved to be too difficult computationally to perform full LTL synthesis. There have been two success stories with LTL synthesis, both having to do with the form of the specification. T...

We explore the potential of continuous local search (CLS) in SAT solving by proposing a novel approach for finding a solution of a hybrid system of Boolean constraints. The algorithm is based on CLS combined with belief propagation on binary decision diagrams (BDDs). Our framework accepts all Boolean constraints that admit compact BDDs, including s...

We present a new synthesis framework based on the on-the-fly DFA construction for LTL over finite traces (LTLf ). Extant approaches rely heavily on the construction of the complete DFA w.r.t. the input LTLf formula, whose size can be doubly exponential to the size of the formula in the worst case. Under those approaches, the synthesis cannot be con...

We revisit here congruence relations for B\"uchi automata, which play a central role in the automata-based verification. The size of the classical congruence relation is in $3^{\mathcal{O}(n^2)}$, where $n$ is the number of states of a given B\"uchi automaton $\mathcal{A}$. Here we present improved congruence relations that can be exponentially mor...

Several problems in planning and reactive synthesis can be reduced to the analysis of two-player quantitative graph games. Optimization is one form of analysis. We argue that in many cases it may be better to replace the optimization problem with the satisficing problem , where instead of searching for optimal solutions, the goal is to search for s...

Edward P. Djerejian, Director and Moshe Y. Vardi, Faculty Scholar at the Baker Institute for Public PolicyHouston, TX, explore the Future of Think Tanks and Policy Advice in the United States.

Several problems in planning and reactive synthesis can be reduced to the analysis of two-player quantitative graph games. {\em Optimization} is one form of analysis. We argue that in many cases it may be better to replace the optimization problem with the {\em satisficing problem}, where instead of searching for optimal solutions, the goal is to s...

We introduce an extension of Strategy Logic for the imperfect-information setting, called SL ii 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 t...

The problem of finding pure strategy Nash equilibria in multiagent concurrent games with finite-horizon temporal goals has received some recent attention. Earlier work solved this problem through the use of Rabin automata. In this work, we take advantage of the finite-horizon nature of the agents' goals and show that checking for and finding pure s...

Following increasing public concern over the ethical and social implications of contemporary technology, computer science departments around the world have recently increased their efforts to incorporate ethics into their educational curriculum. For our redesigned undergraduate course on Computer Ethics at Rice University, in addition to teaching v...

The automata-theoretic approach advocates reducing problems in an application domain to those in automata theory. When there are multiple paths for the reduction, leaving the realm of application and entering that of automata as early as possible should be preferred, to take full advantages of the abundant algorithmic techniques from the latter. Th...

There are no silver bullets in algorithm design, and no single algorithmic idea is powerful and flexible enough to solve every computational problem. Nor are there silver bullets in algorithm analysis, as the most enlightening method for analyzing an algorithm often depends on the problem and the application. However, typical algorithms courses rel...

We explore the potential of continuous local search (CLS) in SAT solving by proposing a novel approach for finding a solution of a hybrid system of Boolean constraints. The algorithm is based on CLS combined with belief propagation on binary decision diagrams (BDDs). Our framework accepts all Boolean constraints that admit compact BDDs, including s...

The matrix permanent belongs to the complexity class #P-Complete. It is generally believed to be computationally infeasible for large problem sizes, and significant research has been done on approximation algorithms for the matrix permanent. We present an implementation and detailed runtime analysis of one such Markov Chain Monte Carlo (MCMC) based...

LTL synthesis is the problem of synthesizing a reactive system from a formal specification in Linear Temporal Logic. The extension of allowing for partial observability, where the system does not have direct access to all relevant information about the environment, allows generalizing this problem to a wider set of real-world applications, but the...

Many systems are naturally modeled as Markov Decision Processes (MDPs), combining probabilities and strategic actions. Given a model of a system as an MDP and some logical specification of system behavior, the goal of synthesis is to find a policy that maximizes the probability of achieving this behavior. A popular choice for defining behaviors is...

Computational learning theory states that many classes of boolean formulas are learnable in polynomial time. This paper addresses the understudied subject of how, in practice, such formulas can be learned by deep neural networks. Specifically, we analyse boolean formulas associated with the decision version of combinatorial optimisation problems, m...

We propose a unifying dynamic-programming framework to compute exact literal-weighted model counts of formulas in conjunctive normal form. At the center of our framework are project-join trees, which specify efficient project-join orders to apply additive projections (variable eliminations) and joins (clause multiplications). In this framework, mod...

We propose a unifying dynamic-programming framework to compute exact literal-weighted model counts of formulas in conjunctive normal form. At the center of our framework are project-join trees, which specify efficient project-join orders to apply additive projections (variable eliminations) and joins (clause multiplications). In this framework, mod...

Reactive synthesis is the problem of automatically constructing a reactive system from a formal specification, with the guarantee that the executions of the system align with the specification. The specification is often described in temporal logic. Some types of specifications can be converted into deterministic finite automata (DFA) as an interme...

A key problem in constrained random verification (CRV) concerns generation of input stimuli that result in good coverage of the system's runs in targeted corners of its behavior space. Existing CRV solutions however provide no formal guarantees on the distribution of the system's runs. In this paper, we take a first step towards solving this proble...

Linear Temporal Logic over finite traces (LTLf) was proposed in 2013 and has attracted increasing interest around the AI community. Though the theoretic basis for LTLf has been thoroughly explored since that time, there are still few algorithmic tools that are able to provide an efficient reasoning strategy for LTLf. In this paper, we present a SAT...

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 t...

In synthesis, assumption are constraints on the environments that
rule out certain environment behaviors. A key observation is that
even if we consider a system with LTLf goals on finite traces,
assumptions need to be expressed considering infinite traces, using
LTL on infinite traces, since the decision to stop the trace is
controlled by the agent...

Prompt-LTL extends Linear Temporal Logic with a bounded version of the ``eventually'' operator to express temporal requirements such as bounding waiting times. We study assume-guarantee synthesis for prompt-LTL: the goal is to construct a system such that for all environments satisfying a first prompt-LTL formula (the assumption) the system compose...

Neural-symbolic computing has now become the subject of interest of both academic and industry research laboratories. Graph Neural Networks (GNNs) 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. Th...

A promising new algebraic approach to weighted model counting makes use of tensor networks, following a reduction from weighted model counting to tensor-network contraction. Prior work has focused on analyzing the single-core performance of this approach, and demonstrated that it is an effective addition to the current portfolio of weighted-model-c...

In this work, we exploit the power of unambiguity for the complementation problem of B\"uchi automata by utilizing reduced run directed acyclic graphs (DAGs) over infinite words, in which each vertex has at most one predecessor. Given a B\"uchi automaton with n states and a finite degree of ambiguity, we show that the number of states in the comple...

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 LTLƒ 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 a...

LTLf synthesis is the automated construction of a reactive system from a high-level description, expressed in LTLf, of its finite-horizon behavior. So far, the conversion of LTLf formulas to deterministic finite-state automata (DFAs) has been identified as the primary bottleneck to the scalabity of synthesis. Recent investigations have also shown t...

The Boolean SATisfiability problem (SAT) is of central importance in computer science. Although SAT is known to be NP-complete, progress on the engineering side—especially that of Conflict-Driven Clause Learning (CDCL) and Local Search SAT solvers—has been remarkable. Yet, while SAT solvers, aimed at solving industrial-scale benchmarks in Conjuncti...

We present an algorithm to compute exact literal-weighted model counts of Boolean formulas in Conjunctive Normal Form. Our algorithm employs dynamic programming and uses Algebraic Decision Diagrams as the main data structure. We implement this technique in ADDMC, a new model counter. We empirically evaluate various heuristics that can be used with...

SAT-based techniques comprise the state-of-the-art in functional verification of safety-critical hardware and software, including IC3/PDR-based model checking and Bounded Model Checking (BMC). BMC is the incontrovertible best method for unsafety checking, aka bug-finding. Complementary Approximate Reachability (CAR) and IC3/PDR complement BMC for b...

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 t...

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...