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We develop model checking algorithms for Temporal Stream Logic (TSL) and Hyper Temporal Stream Logic (HyperTSL) modulo theories. TSL extends Linear Temporal Logic (LTL) with memory cells, functions and predicates, making it a convenient and expressive logic to reason over software and other systems with infinite data domains. HyperTSL further extends TSL to the specification of hyperproperties - properties that relate multiple system executions. As such, HyperTSL can express information flow policies like noninterference in software systems. We augment HyperTSL with theories, resulting in HyperTSL(T),and build on methods from LTL software verification to obtain model checking algorithms for TSL and HyperTSL(T). This results in a sound but necessarily incomplete algorithm for specifications contained in the forall*exists* fragment of HyperTSL(T). Our approach constitutes the first software model checking algorithm for temporal hyperproperties with quantifier alternations that does not rely on a finite-state abstraction.

Smart contracts are small but highly security-critical programs that implement wallets, token systems, auctions, crowd funding systems, elections, and other multi-party transactions on the blockchain. A broad range of methods has been developed to ensure that a smart contract is functionally correct. However, smart contracts often additionally need to satisfy certain hyperproperties, such as symmetry, determinism, or an information flow policy. In this paper, we show how a synthesis method for smart contracts can ensure that the contract satisfies its desired hyperproperties. We build on top of a recently developed synthesis approach from specifications in the temporal logic TSL. We present HyperTSL, an extension of TSL for the specification of hyperproperties of infinite-state software. As a preprocessing step, we show how to detect if a hyperproperty has an equivalent formulation as a (simpler) trace property. Finally, we describe how to refine a synthesized contract to adhere to its HyperTSL specification., Comment: published at 36th IEEE Computer Security Foundations Symposium (CSF 2023)

We study satisfiability for HyperLTL with a $\forall^*\exists^*$ quantifier prefix, known to be highly undecidable in general. HyperLTL can express system properties that relate multiple traces (so-called hyperproperties), which are often combined with trace properties that specify functional behavior on single traces. Following this conceptual split, we first define several safety and liveness fragments of $\forall^*\exists^*$ HyperLTL, and characterize the complexity of their (often much easier) satisfiability problem. We then add LTL trace properties as functional specifications. Though (highly) undecidable in many cases, this way of combining "simple" HyperLTL and arbitrary LTL also leads to interesting new decidable fragments. This systematic study of $\forall^*\exists^*$ fragments is complemented by a new (incomplete) algorithm for $\forall\exists^*$-HyperLTL satisfiability., Comment: LICS 2022

Smart contracts are small but highly error-prone programs that implement agreements between multiple parties. We present a reactive synthesis approach for the automatic construction of smart contract state machines. Towards this end, we extend temporal stream logic (TSL) with universally quantified parameters over infinite domains. Parameterized TSL is a convenient logic to specify the temporal control flow, i.e., the correct order of transactions, as well as the data flow of the contract's fields. We develop a two-step approach that 1) synthesizes a finite representation of the - in general - infinite-state system and 2) splits the system into a compact hierarchical architecture that enables the implementation of the state machine in Solidity. We implement the approach in our prototype tool SCSynt, which - within seconds - automatically constructs Solidity code that realizes the specified control flow.

An enforcement mechanism monitors a reactive system for undesired behavior at runtime and corrects the system's output in case it violates the given specification. In this paper, we study the enforcement problem for hyperproperties, i.e., properties that relate multiple computation traces to each other. We elaborate the notion of sound and transparent enforcement mechanisms for hyperproperties in two trace input models: 1) the parallel trace input model, where the number of traces is known a-priori and all traces are produced and processed in parallel and 2) the sequential trace input model, where traces are processed sequentially and no a-priori bound on the number of traces is known. For both models, we study enforcement algorithms for specifications given as formulas in universally quantified HyperLTL, a temporal logic for hyperproperties. For the parallel model, we describe an enforcement mechanism based on parity games. For the sequential model, we show that enforcement is in general undecidable and present algorithms for reasonable simplifications of the problem (partial guarantees or the restriction to safety properties). Furthermore, we report on experimental results of our prototype implementation for the parallel model.

We studied the hyperlogic HyperQPTL, which combines the concepts of trace relations and $\omega$-regularity. We showed that HyperQPTL is very expressive, it can express properties like promptness, bounded waiting for a grant, epistemic properties, and, in particular, any $\omega$-regular property. Those properties are not expressible in previously studied hyperlogics like HyperLTL. At the same time, we argued that the expressiveness of HyperQPTL is optimal in a sense that a more expressive logic for $\omega$-regular hyperproperties would have an undecidable model checking problem. We furthermore studied the realizability problem of HyperQPTL. We showed that realizability is decidable for HyperQPTL fragments that contain properties like promptness. But still, in contrast to the satisfiability problem, propositional quantification does make the realizability problem of hyperlogics harder. More specifically, the HyperQPTL fragment of formulas with a universal-existential propositional quantifier alternation followed by a single trace quantifier is undecidable in general, even though the projection of the fragment to HyperLTL has a decidable realizability problem. Lastly, we implemented the bounded synthesis problem for HyperQPTL in the prototype tool BoSy. Using BoSy with HyperQPTL specifications, we have been able to synthesize several resource arbiters. The synthesis problem of non-linear-time hyperlogics is still open. For example, it is not yet known how to synthesize systems from specifications given in branching-time hyperlogics like HyperCTL$^*$., Comment: International Conference on Computer Aided Verification (CAV 2020)

We study the expressivity and complexity of model checking linear temporal logic with team semantics (TeamLTL). TeamLTL, despite being a purely modal logic, is capable of defining hyperproperties, i.e., properties which relate multiple execution traces. TeamLTL has been introduced quite recently and only few results are known regarding its expressivity and its model checking problem. We relate the expressivity of TeamLTL to logics for hyperproperties obtained by extending LTL with trace and propositional quantifiers (HyperLTL and HyperQPTL). By doing so, we obtain a number of model checking results for TeamLTL and identify its undecidability frontier. In particular, we show decidability of model checking of the so-called left-flat fragment of any downward closed TeamLTL-extension. Moreover, we establish that the model checking problem of TeamLTL with Boolean disjunction and inclusion atoms is undecidable.

Hyperproperties, which generalize trace properties by relating multiple traces, are widely studied in information-flow security. Recently, a number of logics for hyperproperties have been proposed, and there is a need to understand their decidability and relative expressiveness. The new logics have been obtained from standard logics with two principal extensions: temporal logics, like LTL and CTL$^*$, have been generalized to hyperproperties by adding variables for traces or paths. First-order and second-order logics, like monadic first-order logic of order and MSO, have been extended with the equal-level predicate. We study the impact of the two extensions across the spectrum of linear-time and branching-time logics, in particular for logics with quantification over propositions. The resulting hierarchy of hyperlogics differs significantly from the classical hierarchy, suggesting that the equal-level predicate adds more expressiveness than trace and path variables. Within the hierarchy of hyperlogics, we identify new boundaries on the decidability of the satisfiability problem. Specifically, we show that while HyperQPTL and HyperCTL$^*$ are both undecidable in general, formulas within their $\exists^*\forall^*$ fragments are decidable., Comment: Originally published at LICS 2019