Computer Science

We propose a graph-based extension of Boolean logic called Boolean Graph Logic (BGL). Construing formula trees as the cotrees of cographs, we may state semantic notions such as evaluation and entailment in purely graph-theoretic terms, whence we recover the definition of BGL. Naturally, it is conservative over usual Boolean logic. Our contributions are the following: (1) We give a natural semantics of BGL based on Boolean relations, i.e. it is a multivalued semantics, and show adequacy of this semantics for the corresponding notions of entailment. (2) We show that the complexity of evaluation is NP-complete for arbitrary graphs (as opposed to ALOGTIME-complete for formulas), while entailment is Π p 2 -complete (as opposed to coNP-complete for formulas). (3) We give a 'recursive' algorithm for evaluation by induction on the modular decomposition of graphs. (Though this is not polynomial-time, cf. point (2) above). (4) We characterise evaluation in a game-theoretic setting, in terms of both static and sequentical strategies, extending the classical notion of positional game forms beyond cographs. (5) We give an axiomatisation of BGL, inspired by deep-inference proof theory, and show soundness and completeness for the corresponding notions of entailment. One particular feature of the graph-theoretic setting is that it escapes certain no-go theorems such as a recent result of Das and Strassburger, that there is no linear axiomatisation of the linear fragment of Boolean logic (equivalently the multiplicative fragment of Japaridze's Computability Logic or Blass' game semantics for Mutliplicative Linear Logic).

Shape analysis is of great importance for the verification of the correctness and memory-safety of heap-manipulating programs, yet such analyses have been shown to be highly difficult problems. The integration of separation logic into shape analyses has improved the effectiveness of the techniques, but the most significant advancement in this area is bi-abductive inference. Enabled by separation logic, bi-abduction - a combination of abductive inference and frame inference - is the key enabler for compositional reasoning, helping to scale up verification significantly. Indeed, the success of bi-abduction has led to the development of Infer, the tool used daily to verify Facebook's codebase of millions of lines of code. However, this success currently stays largely within the shape domain. To extend this impact towards the combination of shape and arithmetic domains, in this work, we present a novel one-stage bi-abductive procedure for a combination of data structures and ordering values. The procedure is designed in the spirit of the Unfold-and-Match paradigm where the inference is utilized to derive any mismatched portion. We have also implemented a prototype solver, based on the Cyclist library, and demonstrate its capabilities over a range of benchmarks from the SL-COMP competition. The experimental results show that our proposal shows promise for the specification inference in an automated verification of heap-manipulating programs.

Register automata are a basic model of computation over infinite alphabets. Fresh-register automata extend register automata with the capability to generate fresh symbols in order to model computational scenarios involving name creation. This paper investigates the complexity of the bisimilarity problem for classes of register and fresh-register automata. We examine all main disciplines that have appeared in the literature: general register assignments; assignments where duplicate register values are disallowed; and assignments without duplicates in which registers cannot be empty. In the general case, we show that the problem is EXPTIME-complete. However, the absence of duplicate values in registers enables us to identify inherent symmetries inside the associated bisimulation relations, which can be used to establish a polynomial bound on the depth of Attacker-winning strategies. Furthermore, they enable a highly succinct representation of the corresponding bisimulations. By exploiting results from group theory and computational group theory, we can then show solvability in PSPACE and NP respectively for the latter two register disciplines. In each case, we find that freshness does not affect the complexity class of the problem. The results allow us to close a complexity gap for language equivalence of deterministic register automata. We show that deterministic language inequivalence for the no-duplicates fragment is NP-complete, which disproves an old conjecture of Sakamoto. Finally, we discover that, unlike in the finite-alphabet case, the addition of pushdown store makes bisimilarity undecidable, even in the case of visibly pushdown storage.

Description logics (DLs) are a suitable formalism for representing knowledge about domains in which objects are described not only by attributes but also by binary relations between objects. Fuzzy extensions of DLs can be used for such domains when data and knowledge about them are vague and imprecise. One of the possible ways to specify classes of objects in such domains is to use concepts in fuzzy DLs. As DLs are variants of modal logics, indiscernibility in DLs is characterized by bisimilarity. The bisimilarity relation of an interpretation is the largest auto-bisimulation of that interpretation. In DLs and their fuzzy extensions, such equivalence relations can be used for concept learning. In this paper, we define and study fuzzy bisimulation and bisimilarity for fuzzy DLs under the Gödel semantics, as well as crisp bisimulation and strong bisimilarity for such logics extended with involutive negation. The considered logics are fuzzy extensions of the DL ALC reg (a variant of PDL) with additional features among inverse roles, nominals, (qualified or unqualified) number restrictions, the universal role, local reflexivity of a role and involutive negation. We formulate and prove results on invariance of concepts under fuzzy (resp. crisp) bisimulation, conditional invariance of fuzzy TBoxex/ABoxes under bisimilarity (resp. strong bisimilarity), and the Hennessy-Milner property of fuzzy (resp. crisp) bisimulation for fuzzy DLs without (resp. with) involutive negation under the Gödel semantics. Apart from these fundamental results, we also provide results on using fuzzy bisimulation to separate the expressive powers of fuzzy DLs, as well as results on using strong bisimilarity to minimize fuzzy interpretations.

In this paper, we present Bitwuzla, our Satisfiability Modulo Theories (SMT) solver for the theories of bit-vectors, floating-points, arrays and uninterpreted functions and their combinations. We discuss selected features and provide details of its configuration and participation in the 2020 edition of the annual SMT competition.

In the blockchain-based, distributed computing platform Ethereum, programs called smart contracts are compiled to bytecode and executed on the Ethereum Virtual Machine (EVM). Executing EVM bytecode is subject to monetary fees---a clear optimization target. Our aim is to superoptimize EVM bytecode by encoding the operational semantics of EVM instructions as SMT formulas and leveraging a constraint solver to automatically find cheaper bytecode. We implement this approach in our EVM Bytecode SuperOptimizer ebso and perform two large scale evaluations on real-world data sets.

We generalize the validity criterion for the infinitary proof system of the multiplicative additive linear logic with fixed points. Our criterion is designed to take into account axioms and cuts. We show that it is sound and enjoys the cut elimination property. We finally study its decidability properties, and prove that it is undecidable in general but becomes decidable under some restrictions.

We introduce a new game-theoretic semantics (GTS) for the modal mu-calculus. Our so-called bounded GTS replaces parity games with alternative evaluation games where only finite paths arise; infinite paths are not needed even when the considered transition system is infinite. The novel games offer alternative approaches to various constructions in the framework of the mu-calculus. For example, they have already been successfully used as a basis for an approach leading to a natural formula size game for the logic. While our main focus is introducing the new GTS, we also consider some applications to demonstrate its uses. For example, we consider a natural model transformation procedure that reduces model checking games to checking a single, fixed formula in the constructed models, and we also use the GTS to identify new alternative variants of the mu-calculus with PTime model checking.

This paper provides a formal model for the burden of persuasion in dialogues, and in particular, in legal proceedings. The model shows how an allocation of the burden of persuasion may induce single outcomes in dialectical contexts in which, without such an allocation, the status of conflicting arguments would remain undecided. Our approach is based on a two-stage labelling. The first-stage labelling determines what arguments are accepted, rejected or undecided, regardless of the allocation of burden. The second-stage labelling revises the dialectical status of first-stage undecided arguments, according to burdens of persuasion. The labelling is finally extended in such a way as to obtain a complete labelling. Our model combines two ideas that have emerged in the debate on the burden of persuasion: the idea that the burden of persuasion determines the solution of conflicts between arguments, and the idea that its satisfaction depends on the dialectical status of the arguments concerned. Our approach also addresses inversions of the burden of persuasion, namely, cases in which the burden of persuasion over an argument does not extend to its subarguments.

Over the last two decades, we have seen a dramatic improvement in the efficiency of conflict-driven clause-learning Boolean satisfiability (CDCL SAT) solvers on industrial problems from a variety of domains. The availability of such powerful general-purpose search tools as SAT solvers has led many researchers to propose SAT-based methods for cryptanalysis, including techniques for finding collisions in hash functions and breaking symmetric encryption schemes. Most of the previously proposed SAT-based cryptanalysis approaches are blackbox techniques, in the sense that the cryptanalysis problem is encoded as a SAT instance and then a CDCL SAT solver is invoked to solve the said instance. A weakness of this approach is that the encoding thus generated may be too large for any modern solver to solve efficiently. Perhaps a more important weakness of this approach is that the solver is in no way specialized or tuned to solve the given instance. To address these issues, we propose an approach called CDCL(Crypto) (inspired by the CDCL(T) paradigm in Satisfiability Modulo Theory solvers) to tailor the internal subroutines of the CDCL SAT solver with domain-specific knowledge about cryptographic primitives. Specifically, we extend the propagation and conflict analysis subroutines of CDCL solvers with specialized codes that have knowledge about the cryptographic primitive being analyzed by the solver. We demonstrate the power of this approach in the differential path and algebraic fault analysis of hash functions. Our initial results are very encouraging and reinforce the notion that this approach is a significant improvement over blackbox SAT-based cryptanalysis.