# Computer Science - Logic in Computer Science Publications (50)

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## Computer Science - Logic in Computer Science Publications

We extend the constructive dependent type theory of the Logical Framework $\mathsf{LF}$ with monadic, dependent type constructors indexed with predicates over judgements, called Locks. These monads capture various possible proof attitudes in establishing the judgment of the object logic encoded by an $\mathsf{LF}$ type. Standard examples are factoring-out the verification of a constraint or delegating it to an external oracle, or supplying some non-apodictic epistemic evidence, or simply discarding the proof witness of a precondition deeming it irrelevant. Read More

We present PORTHOS, the first tool that discovers porting bugs in performance-critical code. PORTHOS takes as input a program, the memory model of the source architecture for which the program has been developed, and the memory model of the targeted architecture. If the code is not portable, PORTHOS finds a porting bug in the form of an unexpected execution - an execution that is consistent with the target but inconsistent with the source memory model. Read More

In this paper we study possibilities of interpolation and symbol elimination in extensions of a theory ${\cal T}_0$ with additional function symbols whose properties are axiomatised using a set of clauses. We analyze situations in which we can perform such tasks in a hierarchical way, relying on existing mechanisms for symbol elimination in ${\cal T}_0$. This is for instance possible if the base theory allows quantifier elimination. Read More

In this paper, we study the notion of admissibility for randomised strategies in concurrent games. Intuitively, an admissible strategy is one where the player plays `as well as possible', because there is no other strategy that dominates it, i.e. Read More

We consider the task of enumerating and counting answers to $k$-ary conjunctive queries against relational databases that may be updated by inserting or deleting tuples. We exhibit a new notion of q-hierarchical conjunctive queries and show that these can be maintained efficiently in the following sense. During a linear time preprocessing phase, we can build a data structure that enables constant delay enumeration of the query results; and when the database is updated, we can update the data structure and restart the enumeration phase within constant time. Read More

We consider the problem of deciding the satisfiability of quantifier-free formulas in the theory of finite sets with cardinality constraints. Sets are a common high-level data structure used in programming; thus, such a theory is useful for modeling program constructs directly. More importantly, sets are a basic construct of mathematics and thus natural to use when formalizing the properties of computational systems. Read More

Reducing interaction nets without any specific strategy benefits from constant time per step. On the other hand, a canonical reduction step for weak reduction to interface normal form is linear by depth of terms. In this paper, we refine the weak interaction calculus to reveal the actual cost of its reduction. Read More

Modern distributed systems often rely on so called weakly-consistent databases, which achieve scalability by sacrificing the consistency guarantee of distributed transaction processing. Such databases have been formalised in two different styles, one based on abstract executions and the other based on dependency graphs. The choice between these styles has been made according to intended applications: the former has been used to specify and verify the implementation of these databases, and the latter to prove properties of programs running on top of the databases. Read More

Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic that gives an account of layering. The logic is a bunched system, combining the usual intuitionistic connectives, together with a non-commutative, non-associative conjunction (used to capture layering) and its associated implications. Read More

In order to study the axiomatization of the if-then-else construct over possibly non-halting programs and tests, the notion of $C$-sets was introduced in the literature by considering the tests from an abstract $C$-algebra. This paper extends the notion of $C$-sets to $C$-monoids which include the composition of programs as well as composition of programs with tests. For the class of $C$-monoids where the $C$-algebras are adas a canonical representation in terms of functional $C$-monoids is obtained. Read More

A MATLAB toolbox is presented, with the goal of checking occurrences of design errors typically found in fixed-point digital systems, considering finite word-length effects. In particular, the present toolbox works as a front-end to a recently introduced verification tool, known as Digital-System Verifier, and checks overflow, limit cycle, quantization, stability, and minimum phase errors, in digital systems represented by transfer-function and state-space equations. It provides a command-line version, with simplified access to specific functions, and a graphical-user interface, which was developed as a MATLAB application. Read More

We study the problem of enumerating the satisfying valuations of a circuit while bounding the delay, i.e., the time needed to compute each successive valuation. Read More

Branching bisimilarity on normed Basic Process Algebra (BPA) was claimed to be EXPTIME-hard in previous papers without any explicit proof. Recently it is reminded by Jan\v{c}ar that the claim is not so dependable. In this paper, we develop a new complete proof for EXPTIME-hardness of branching bisimilarity on normed BPA. Read More

Clause-elimination procedures that simplify formulas in conjunctive normal form play an important role in modern SAT solving. Before or during the actual solving process, such procedures identify and remove clauses that are irrelevant to the solving result. These simplifications usually rely on so-called redundancy properties that characterize cases in which the removal of a clause does not affect the satisfiability status of a formula. Read More

The beyond worst-case synthesis problem was introduced recently by Bruy\`ere et al. [BFRR14]: it aims at building system controllers that provide strict worst-case performance guarantees against an antagonistic environment while ensuring higher expected performance against a stochastic model of the environment. Our work extends the framework of [BFRR14] and follow-up papers, which focused on quantitative objectives, by addressing the case of $\omega$-regular conditions encoded as parity objectives, a natural way to represent functional requirements of systems. Read More

**Affiliations:**

^{1}LIAFA,

^{2}LIAFA,

^{3}LaBRI

We develop an algebraic model for recognizing languages of words indexed by countable linear orderings. This notion of recognizability is effectively equivalent to definability in monadic second-order (MSO) logic. The proofs also imply the first known collapse result for MSO logic over countable linear orderings. Read More

Information systems with witnesses have been introduced in [D. Spreen. Generalised information systems capture L-domains. Read More

The present paper introduces an intrinsic notion of "(effective) computability" in game semantics motivated by the fact that strategies in game semantics have been defined recursive if they are "computable in an extrinsic sense", i.e., they are representable by partial recursive functions, and so it has been difficult to regard game semantics as an autonomous foundation of computation. Read More

Calude et al. have given the first algorithm for solving parity games in quasi-polynomial time, where previously the best algorithms were mildly subexponential. We combine the succinct counting technique of Calude et al. Read More

This thesis introduces the idea of two-level type theory, an extension of Martin-L\"of type theory that adds a notion of strict equality as an internal primitive. A type theory with a strict equality alongside the more conventional form of equality, the latter being of fundamental importance for the recent innovation of homotopy type theory (HoTT), was first proposed by Voevodsky, and is usually referred to as HTS. Here, we generalise and expand this idea, by developing a semantic framework that gives a systematic account of type formers for two-level systems, and proving a conservativity result relating back to a conventional type theory like HoTT. Read More

We present a denotational account of dynamic allocation of potentially cyclic memory cells using a monad on a functor category. We identify the collection of heaps as an object in a different functor category equipped with a monad for adding hiding/encapsulation capabilities to the heaps. We derive a monad for full ground references supporting effect masking by applying a state monad transformer to the encapsulation monad. Read More

We investigate the extension of Monadic Second Order logic, interpreted over infinite words and trees, with generalized "for almost all" quantifiers interpreted using the notions of Baire category and Lebesgue measure. Read More

Usually, it is the software manufacturer who employs verification or testing to ensure that the software embedded in a device meets its main objectives. However, these days we are confronted with the situation that economical or technological reasons might make a manufacturer become interested in the software slightly deviating from its main objective for dubious reasons. Examples include lock-in strategies and the $\mathrm{NO}_x$ emission scandals in automotive industry. Read More

In this contribution we investigate several extensions of the powerset that comprise arbitrarily nested subsets, and call them superpower set. This allows the definition of graphs with possibly infinitely nested nodes. additionally we define edges that are incident to edges. Read More

Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. The resulting notion of relational convolution leads to generalised binary and unary modal operators for qualitative and quantitative models, and to more conventional variants, when ternary relations arise from identies over partial semigroups. Read More

The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification languages and systems. This paper is a formal study of some of the most common forms of inductive definitions found in scientific text: monotone inductive definition, definition by induction over a well-founded order and iterated inductive definitions. We define a logic of definitions offering a uniform formal syntax to express definitions of the different sorts, and we define its semantics by a faithful formalization of the induction process. Read More

The output of an automated theorem prover is usually presented by using a text format, they are often too heavy to be understood. In model checking setting, it would be helpful if one can observe the structure of models and the verification procedures. A 3D visualization tool (\textsf{VMDV}) is proposed in this paper to address these problems. Read More

A cyclic proof system generalises the standard notion of a proof as a finite tree of locally sound inferences by allowing proof objects to be potentially infinite. Regular infinite proofs can be finitely represented as graphs. To preclude spurious cyclic reasoning, cyclic proof systems come equipped with a well-founded notion of 'size' for the models that interpret their logical statements. Read More

This note is meant to invite the reader to consider interaction nets, a relatively recently discovered model of computation, as a possible alternative for cellular automata which are often employed as the basis for digital physics. Defined as graph-like structures (in contrast to the grids for cellular automata), interaction nets possess a set of interesting properties, such as locality, linearity, and strong confluence, which together result in so-called clockless computation in the sense that they do not require any global clock in order to operate. We believe that an attempt of using interaction nets as a replacement for cellular automata may lead to a new view in digital physics. Read More

In program algebra, an algebraic theory of single-pass instruction sequences, three congruences on instruction sequences are paid attention to: instruction sequence congruence, structural congruence, and behavioural congruence. Sound and complete axiom systems for the first two congruences were already given in early papers on program algebra. The current paper is the first one that is concerned with an axiom system for the third congruence. Read More

Many security protocols rely on the assumptions on the physical properties in which its protocol sessions will be carried out. For instance, Distance Bounding Protocols take into account the round trip time of messages and the transmission velocity to infer an upper bound of the distance between two agents. We classify such security protocols as Cyber-Physical. Read More

We revisit a fundamental result in real-time verification, namely that the binary reachability relation between configurations of a given timed automaton is definable in linear arithmetic over the integers and reals. In this paper we give a new and simpler proof of this result, building on the well-known reachability analysis of timed automata involving difference bound matrices. Using this new proof, we give an exponential-space procedure for model checking the reachability fragment of the logic parametric TCTL. Read More

LP$^{\supset,\mathsf{F}}$ is a three-valued paraconsistent propositional logic which is essentially the same as J3. It has most properties that have been proposed as desirable properties of a reasonable paraconsistent propositional logic. However, it follows easily from already published results that there are exactly 8192 different three-valued paraconsistent propositional logics that have the properties concerned. Read More

We argue that the implementation and verification of compilers for functional programming languages are greatly simplified by employing a higher-order representation of syntax known as Higher-Order Abstract Syntax or HOAS. The underlying idea of HOAS is to use a meta-language that provides a built-in and logical treatment of binding related notions. By embedding the meta-language within a larger programming or reasoning framework, it is possible to absorb the treatment of binding structure in the object language into the meta-theory of the system, thereby greatly simplifying the overall implementation and reasoning processes. Read More

Logic of Behaviour in Context (LBC) is a spatio-temporal logic for expressing properties of continuous-state processes, such as biochemical reaction networks. LBC builds on the existing Metric Interval Temporal Logic (MITL) and adds a "context modality" that explores the behaviour of a system when composed with an external process. LBC models are terms of the Continuous {\pi}-Calculus (c{\pi}), a process algebra with continuous state space. Read More

We introduce a novel parsing concept called local lexing. It integrates the classically separated stages of lexing and parsing by allowing lexing to be dependent upon the parsing progress and by providing a simple mechanism for constraining lexical ambiguity. This makes it possible for language design to be composable not only at the level of context-free grammars, but also at the lexical level. Read More

In this paper we consider the most common ABox reasoning services for the description logic $\dlssx$ ($\shdlssx$, for short) and prove their decidability via a reduction to the satisfiability problem for the set-theoretic fragment \flqsr. $\shdlssx$ is a very expressive description logic admitting various concept and role constructs, and datatypes, that allows one to represent rule based languages such as SWRL. Decidability results are achieved by defining a generalized version of the conjunctive query answering problem, called HOCQA (Higher Order Conjunctive Query Answering), that can be instantiated to the most widespread ABox reasoning tasks. Read More

Affine $$\lambda$$-terms are $$\lambda$$-terms in which each bound variable occurs at most once and linear $$\lambda$$-terms are $$\lambda$$-terms in which each bound variables occurs once. and only once. In this paper we count the number of closed affine $$\lambda$$-terms of size $n$, closed linear $$\lambda$$-terms of size $n$, affine $$\beta$$-normal forms of size $n$ and linear $$\beta$$-normal forms of ise $n$, for different ways of measuring the size of $$\lambda$$-terms. Read More

We propose a formal approach for relating abstract separation logic library specifications with the trace properties they enforce on interactions between a client and a library. Separation logic with abstract predicates enforces a resource discipline that constrains when and how calls may be made between a client and a library. Intuitively, this can enforce a protocol on the interaction trace. Read More

Parameterized algorithms are a way to solve hard problems more efficiently, given that a specific parameter of the input is small. In this paper, we apply this idea to the field of answer set programming (ASP). To this end, we propose two kinds of graph representations of programs to exploit their treewidth as a parameter. Read More

Proof schemata are a variant of LK-proofs able to simulate various induction schemes in first-order logic by adding so called proof links to the standard first-order LK-calculus. Proof links allow proofs to reference proofs thus giving proof schemata a recursive structure. Unfortunately, applying reductive cut- elimination is non-trivial in the presence of proof links. Read More

In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS 2016) that uses equality relations $t \equiv_\varepsilon s$ indexed by rationals, expressing that `$t$ is approximately equal to $s$ up to an error $\varepsilon$'. Read More

Spark is a new promising platform for scalable data-parallel computation. It provides several high-level application programming interfaces (APIs) to perform parallel data aggregation. Since execution of parallel aggregation in Spark is inherently non-deterministic, a natural requirement for Spark programs is to give the same result for any execution on the same data set. Read More

This paper considers quasi-reductivity - essentially, the property that an evaluation cannot get "stuck" due to a missing case in pattern matching - in the context of term rewriting with logical constraints. Read More

Optimization Modulo Theories (OMT) is an extension of SMT which allows for finding models that optimize given objectives. (Partial weighted) MaxSMT --or equivalently OMT with Pseudo-Boolean objective functions, OMT+PB-- is a very-relevant strict subcase of OMT. We classify existing approaches for MaxSMT or OMT+PB in two groups: MaxSAT-based approaches exploit the efficiency of state-of-the-art MAXSAT solvers, but they are specific-purpose and not always applicable; OMT-based approaches are general-purpose, but they suffer from intrinsic inefficiencies on MaxSMT/OMT+PB problems. Read More

The CEGAR loop in software model checking notoriously diverges when the abstraction refinement procedure does not derive a loop invariant. An abstraction refinement procedure based on an SMT solver is applied to a trace, i.e. Read More

**Affiliations:**

^{1}Tohoku University, Japan

Getting polymorphism and effects such as mutation to live together in the same language is a tale worth telling, under the recurring refrain of copying vs. sharing. We add new stanzas to the tale, about the ordeal to generate code with polymorphism and effects, and be sure it type-checks. Read More

**Affiliations:**

^{1}University of Warsaw

We present a new approach to the following meta-problem: given a quantitative property of trees, design a type system such that the desired property for the tree generated by an infinitary ground lambda-term corresponds to some property of a derivation of a type for this lambda-term, in this type system. Our approach is presented in the particular case of the language finiteness problem for nondeterministic higher-order recursion schemes (HORSes): given a nondeterministic HORS, decide whether the set of all finite trees generated by this HORS is finite. We give a type system such that the HORS can generate a tree of an arbitrarily large finite size if and only if in the type system we can obtain derivations that are arbitrarily large, in an appropriate sense; the latter condition can be easily decided. Read More

**Authors:**Mario Coppo

^{1}, Mariangiola Dezani-Ciancaglini

^{2}, Alejandro Díaz-Caro

^{3}, Ines Margaria

^{4}, Maddalena Zacchi

^{5}

**Affiliations:**

^{1}Università di Torino,

^{2}Università di Torino,

^{3}CONICET and Universidad Nacional de Quilmes,

^{4}Università di Torino,

^{5}Università di Torino

This paper deals with retraction - intended as isomorphic embedding - in intersection types building left and right inverses as terms of a lambda calculus with a bottom constant. The main result is a necessary and sufficient condition two strict intersection types must satisfy in order to assure the existence of two terms showing the first type to be a retract of the second one. Moreover, the characterisation of retraction in the standard intersection types is discussed. Read More

**Affiliations:**

^{1}Imperial College London, UK

We study the strict type assignment for lambda-mu that is presented in [van Bakel'16]. We define a notion of approximants of lambda-mu-terms, show that it generates a semantics, and that for each typeable term there is an approximant that has the same type. We show that this leads to a characterisation via assignable types for all terms that have a head normal form, and to one for all terms that have a normal form, as well as to one for all terms that are strongly normalisable. Read More