arXiv subjects

Yaron Velner

Publications and source records attributed to Yaron Velner.

14 recordsLinked to original sources

arXiv2024

SoK: Liquid Staking Tokens (LSTs) and Emerging Trends in Restaking

Liquid staking and restaking represent recent innovations in Decentralized Finance (DeFi) that garnered user interest and capital. Liquid Staking Tokens (LSTs), tokenized representations of staked tokens on Proof-of-Stake (PoS) blockchains, are the leading staking method. LSTs offer users the ability to earn staking rewards while maintaining liquidity, enabling seamless integration into DeFi protocols and free tradeability. Restaking builds upon this concept by allowing staked tokens, LSTs or native Bitcoin tokens to secure additional protocols and PoS chains for supplementary rewards. Liquid Restaking Tokens (LRTs) unlock liquidity of restaked assets. This Systematization of Knowledge (SoK) establishes a comprehensive framework for the technical and economic models of liquid staking protocols. Using this framework, we systematically compare protocols mechanics, including node operator selection, staking reward distribution, and slashing. Our empirical analysis of token performance reveals that protocol design and market dynamics impact token market value. We further present the recent developments in restaking and discuss associated risks and security implications. Lastly, we review the emerging literature on liquid staking and restaking.

cs.CR↗

arXiv2021

Some Complexity Results for Stateful Network Verification

In modern networks, forwarding of packets often depends on the history of previously transmitted traffic. Such networks contain stateful middleboxes, whose forwarding behaviour depends on a mutable internal state. Firewalls and load balancers are typical examples of stateful middleboxes. This work addresses the complexity of verifying safety properties, such as isolation, in networks with finite-state middleboxes. Unfortunately, we show that even in the absence of forwarding loops, reasoning about such networks is undecidable due to interactions between middleboxes connected by unbounded ordered channels. We therefore abstract away channel ordering. This abstraction is sound for safety, and makes the problem decidable. Specifically, safety checking becomes EXPSPACE-complete in the number of hosts and middleboxes in the network. To tackle the high complexity, we identify two useful subclasses of finite-state middleboxes which admit better complexities. The simplest class includes, e.g., firewalls and permits polynomial-time verification. The second class includes, e.g., cache servers and learning switches, and makes the safety problem coNP-complete. Finally, we implement a tool for verifying the correctness of stateful networks.

cs.LO↗

arXiv2018

Ergodic Mean-Payoff Games for the Analysis of Attacks in Crypto-Currencies

Crypto-currencies are digital assets designed to work as a medium of exchange, e.g., Bitcoin, but they are susceptible to attacks (dishonest behavior of participants). A framework for the analysis of attacks in crypto-currencies requires (a) modeling of game-theoretic aspects to analyze incentives for deviation from honest behavior; (b) concurrent interactions between participants; and (c) analysis of long-term monetary gains. Traditional game-theoretic approaches for the analysis of security protocols consider either qualitative temporal properties such as safety and termination, or the very special class of one-shot (stateless) games. However, to analyze general attacks on protocols for crypto-currencies, both stateful analysis and quantitative objectives are necessary. In this work our main contributions are as follows: (a) we show how a class of concurrent mean-payoff games, namely ergodic games, can model various attacks that arise naturally in crypto-currencies; (b) we present the first practical implementation of algorithms for ergodic games that scales to model realistic problems for crypto-currencies; and (c) we present experimental results showing that our framework can handle games with thousands of states and millions of transitions.

cs.CR↗

arXiv2018

Quantitative Analysis of Smart Contracts

Smart contracts are computer programs that are executed by a network of mutually distrusting agents, without the need of an external trusted authority. Smart contracts handle and transfer assets of considerable value (in the form of crypto-currency like Bitcoin). Hence, it is crucial that their implementation is bug-free. We identify the utility (or expected payoff) of interacting with such smart contracts as the basic and canonical quantitative property for such contracts. We present a framework for such quantitative analysis of smart contracts. Such a formal framework poses new and novel research challenges in programming languages, as it requires modeling of game-theoretic aspects to analyze incentives for deviation from honest behavior and modeling utilities which are not specified as standard temporal properties such as safety and termination. While game-theoretic incentives have been analyzed in the security community, their analysis has been restricted to the very special case of stateless games. However, to analyze smart contracts, stateful analysis is required as it must account for the different program states of the protocol. Our main contributions are as follows: we present (i)~a simplified programming language for smart contracts; (ii)~an automatic translation of the programs to state-based games; (iii)~an abstraction-refinement approach to solve such games; and (iv)~experimental results on real-world-inspired smart contracts.

cs.PL↗

arXiv2017

Abstract Interpretation of Stateful Networks

Modern networks achieve robustness and scalability by maintaining states on their nodes. These nodes are referred to as middleboxes and are essential for network functionality. However, the presence of middleboxes drastically complicates the task of network verification. Previous work showed that the problem is undecidable in general and EXPSPACE-complete when abstracting away the order of packet arrival. We describe a new algorithm for conservatively checking isolation properties of stateful networks. The asymptotic complexity of the algorithm is polynomial in the size of the network, albeit being exponential in the maximal number of queries of the local state that a middlebox can do, which is often small. Our algorithm is sound, i.e., it can never miss a violation of safety but may fail to verify some properties. The algorithm performs on-the fly abstract interpretation by (1) abstracting away the order of packet processing and the number of times each packet arrives, (2) abstracting away correlations between states of different middleboxes and channel contents, and (3) representing middlebox states by their effect on each packet separately, rather than taking into account the entire state space. We show that the abstractions do not lose precision when middleboxes may reset in any state. This is encouraging since many real middleboxes reset, e.g., after some session timeout is reached or due to hardware failure.

cs.PL↗

arXiv2016

Minimizing Expected Cost Under Hard Boolean Constraints, with Applications to Quantitative Synthesis

In Boolean synthesis, we are given an LTL specification, and the goal is to construct a transducer that realizes it against an adversarial environment. Often, a specification contains both Boolean requirements that should be satisfied against an adversarial environment, and multi-valued components that refer to the quality of the satisfaction and whose expected cost we would like to minimize with respect to a probabilistic environment. In this work we study, for the first time, mean-payoff games in which the system aims at minimizing the expected cost against a probabilistic environment, while surely satisfying an $\omega$-regular condition against an adversarial environment. We consider the case the $\omega$-regular condition is given as a parity objective or by an LTL formula. We show that in general, optimal strategies need not exist, and moreover, the limit value cannot be approximated by finite-memory strategies. We thus focus on computing the limit-value, and give tight complexity bounds for synthesizing $\epsilon$-optimal strategies for both finite-memory and infinite-memory strategies. We show that our game naturally arises in various contexts of synthesis with Boolean and multi-valued objectives. Beyond direct applications, in synthesis with costs and rewards to certain behaviors, it allows us to compute the minimal sensing cost of $\omega$-regular specifications -- a measure of quality in which we look for a transducer that minimizes the expected number of signals that are read from the input.

cs.FL↗

arXiv2014

Robust Multidimensional Mean-Payoff Games are Undecidable

Mean-payoff games play a central role in quantitative synthesis and verification. In a single-dimensional game a weight is assigned to every transition and the objective of the protagonist is to assure a non-negative limit-average weight. In the multidimensional setting, a weight vector is assigned to every transition and the objective of the protagonist is to satisfy a boolean condition over the limit-average weight of each dimension, e.g., $\LimAvg(x_1) \leq 0 \vee \LimAvg(x_2)\geq 0 \wedge \LimAvg(x_3) \geq 0$. We recently proved that when one of the players is restricted to finite-memory strategies then the decidability of determining the winner is inter-reducible with Hilbert's Tenth problem over rationals (a fundamental long-standing open problem). In this work we allow arbitrary (infinite-memory) strategies for both players and we show that the problem is undecidable.

cs.LO↗

arXiv2014

Visibly Pushdown Modular Games

Games on recursive game graphs can be used to reason about the control flow of sequential programs with recursion. In games over recursive game graphs, the most natural notion of strategy is the modular strategy, i.e., a strategy that is local to a module and is oblivious to previous module invocations, and thus does not depend on the context of invocation. In this work, we study for the first time modular strategies with respect to winning conditions that can be expressed by a pushdown automaton. We show that such games are undecidable in general, and become decidable for visibly pushdown automata specifications. Our solution relies on a reduction to modular games with finite-state automata winning conditions, which are known in the literature. We carefully characterize the computational complexity of the considered decision problem. In particular, we show that modular games with a universal Buchi or co Buchi visibly pushdown winning condition are EXPTIME-complete, and when the winning condition is given by a CARET or NWTL temporal logic formula the problem is 2EXPTIME-complete, and it remains 2EXPTIME-hard even for simple fragments of these logics. As a further contribution, we present a different solution for modular games with finite-state automata winning condition that runs faster than known solutions for large specifications and many exits.

cs.LO↗

arXiv2014

Finite-Memory Strategy Synthesis for Robust Multidimensional Mean-Payoff Objectives

Two-player games on graphs provide the mathematical foundation for the study of reactive systems. In the quantitative framework, an objective assigns a value to every play, and the goal of player 1 is to minimize the value of the objective. In this framework, there are two relevant synthesis problems to consider: the quantitative analysis problem is to compute the minimal (or infimum) value that player 1 can assure, and the boolean analysis problem asks whether player 1 can assure that the value of the objective is at most $ν$ (for a given threshold $ν$). Mean-payoff expression games are played on a multidimensional weighted graph. An atomic mean-payoff expression objective is the mean-payoff value (the long-run average weight) of a certain dimension, and the class of mean-payoff expressions is the closure of atomic mean-payoff expressions under the algebraic operations of $\MAX,\MIN$, numerical complement and $\SUM$. In this work, we study for the first time the strategy synthesis problems for games with robust quantitative objectives, namely, games with mean-payoff expression objectives. While in general, optimal strategies for these games require infinite-memory, in synthesis we are typically interested in the construction of a finite-state system. Hence, we consider games in which player 1 is restricted to finite-memory strategies, and our main contribution is as follows. We prove that for mean-payoff expressions, the quantitative analysis problem is computable, and the boolean analysis problem is inter-reducible with Hilbert's tenth problem over rationals --- a fundamental long-standing open problem in computer science and mathematics.

cs.LO↗

arXiv2013

Hyperplane Separation Technique for Multidimensional Mean-Payoff Games

We consider both finite-state game graphs and recursive game graphs (or pushdown game graphs), that can model the control flow of sequential programs with recursion, with multi-dimensional mean-payoff objectives. In pushdown games two types of strategies are relevant: global strategies, that depend on the entire global history; and modular strategies, that have only local memory and thus do not depend on the context of invocation. We present solutions to several fundamental algorithmic questions and our main contributions are as follows: (1) We show that finite-state multi-dimensional mean-payoff games can be solved in polynomial time if the number of dimensions and the maximal absolute value of the weight is fixed; whereas if the number of dimensions is arbitrary, then problem is already known to be coNP-complete. (2) We show that pushdown graphs with multi-dimensional mean-payoff objectives can be solved in polynomial time. (3) For pushdown games under global strategies both single and multi-dimensional mean-payoff objectives problems are known to be undecidable, and we show that under modular strategies the multi-dimensional problem is also undecidable (whereas under modular strategies the single dimensional problem is NP-complete). We show that if the number of modules, the number of exits, and the maximal absolute value of the weight is fixed, then pushdown games under modular strategies with single dimensional mean-payoff objectives can be solved in polynomial time, and if either of the number of exits or the number of modules is not bounded, then the problem is NP-hard. (4) Finally we show that a fixed parameter tractable algorithm for finite-state multi-dimensional mean-payoff games or pushdown games under modular strategies with single-dimensional mean-payoff objectives would imply the solution of the long-standing open problem of fixed parameter tractability of parity games.

cs.GT↗

arXiv2013

The Complexity of Infinitely Repeated Alternating Move Games

We consider infinite duration alternating move games. These games were previously studied by Roth, Balcan, Kalai and Mansour. They presented an FPTAS for computing an approximated equilibrium, and conjectured that there is a polynomial algorithm for finding an exact equilibrium. We extend their study in two directions: (1) We show that finding an exact equilibrium, even for two-player zero-sum games, is polynomial time equivalent to finding a winning strategy for a (two-player) mean-payoff game on graphs. The existence of a polynomial algorithm for the latter is a long standing open question in computer science. Our hardness result for two-player games suggests that two-player alternating move games are harder to solve than two-player simultaneous move games, while the work of Roth et al., suggests that for $k\geq 3$, $k$-player games are easier to analyze in the alternating move setting. (2) We show that optimal equilibriums (with respect to the social welfare metric) can be obtained by pure strategies, and we present an FPTAS for computing a pure approximated equilibrium that is $δ$-optimal with respect to the social welfare metric. This result extends the previous work by presenting an FPTAS that finds a much more desirable approximated equilibrium. We also show that if there is a polynomial algorithm for mean-payoff games on graphs, then there is a polynomial algorithm that computes an optimal exact equilibrium, and hence, (two-player) mean-payoff games on graphs are inter-reducible with $k$-player alternating move games, for any $k\geq 2$.

cs.GT↗

arXiv2012

The Complexity of Multi-Mean-Payoff and Multi-Energy Games

In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always nonnegative. Multi-mean-payoff and multi-energy games replace individual weights by tuples, and the limit average (resp. running sum) of each coordinate must be (resp. remain) nonnegative. These games have applications in the synthesis of resource-bounded processes with multiple resources. We prove the finite-memory determinacy of multi-energy games and show the inter-reducibility of multimean-payoff and multi-energy games for finite-memory strategies. We also improve the computational complexity for solving both classes of games with finite-memory strategies: while the previously best known upper bound was EXPSPACE, and no lower bound was known, we give an optimal coNP-complete bound. For memoryless strategies, we show that the problem of deciding the existence of a winning strategy for the protagonist is NP-complete. Finally we present the first solution of multi-meanpayoff games with infinite-memory strategies. We show that multi-mean-payoff games with mean-payoff-sup objectives can be decided in NP and coNP, whereas multi-mean-payoff games with mean-payoff-inf objectives are coNP-complete.

cs.GT↗

arXiv2012

The Complexity of Mean-Payoff Automaton Expression

"Quantitative languages are extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of the transition weights. The class of \emph{mean-payoff automaton expressions}, introduced in [1], is a class of quantitative languages, which is robust: it is closed under the four pointwise operations of max, min, sum and numerical complement."[1] In this paper we improve the computational complexity for solving the classical decision problems for mean-payoff automaton expressions: while the previously best known upper bound was 4EXPTIME, and no lower bound was known, we give an optimal PSPACE complete bound. As a consequence we also obtain a conceptually simple algorithm to solve the classical decision problems for mean-payoff automaton expressions.

cs.LO↗

arXiv2012

Mean-Payoff Pushdown Games

Two-player games on graphs is central in many problems in formal verification and program analysis such as synthesis and verification of open systems. In this work we consider solving recursive game graphs (or pushdown game graphs) that can model the control flow of sequential programs with recursion. While pushdown games have been studied before with qualitative objectives, such as reachability and $\omega$-regular objectives, in this work we study for the first time such games with the most well-studied quantitative objective, namely, mean-payoff objectives. In pushdown games two types of strategies are relevant: (1) global strategies, that depend on the entire global history; and (2) modular strategies, that have only local memory and thus does not depend on the context of invocation, but only on the history of the current invocation of the module. Our main results are as follows (1) One-player pushdown games with mean-payoff objectives under global strategies is decidable in polynomial time. (2) Two-player pushdown games with mean-payoff objectives under global strategies is undecidable. (3) One-player pushdown games with mean-payoff objectives under modular strategies is NP-hard. (4) Two-player pushdown games with mean-payoff objectives under modular strategies can be solved in NP (i.e., both one-player and two-player pushdown games with mean-payoff objectives under modular strategies is NP-complete). We also establish the optimal strategy complexity showing that global strategies for mean-payoff objectives require infinite memory even in one-player pushdown games; and memoryless modular strategies are sufficient in two-player pushdown games. Finally we also show that all the problems have the same complexity if the stack boundedness condition is added, where along with the mean-payoff objective the player must also ensure that the stack height is bounded.

cs.LO↗