A correspondence is established between one-variable fragments of (first-order) intermediate logics defined over a fixed countable linear frame and Gödel modal logics defined over many-valued equivalence relations with values in a closed subset of the real unit interval. It is also shown that each of these logics can be interpreted in the one-variable fragment of the corresponding constant domain intermediate

In this paper we introduce a language of first-order hybrid logic in which function symbols are interpreted by partial functions and prove a number of completeness results. Syntactically, our language builds on the basic propositional hybrid language, has a primitive unary predicate symbol DEN which tests whether a term denotes or not, and permits satisfaction operators to rigidify predicate and function

We investigate language interpretations of two extensions of the Lambek calculus: with additive conjunction and disjunction and with additive conjunction and the unit constant. For extensions with additive connectives, we show that conjunction and disjunction behave differently. Adding both of them leads to incompleteness due to the distributivity law. We show that with conjunction only no issues with

We give a computational interpretation to an abstract formulation of Krull's theorem, by analysing its classical proof based on Zorn's lemma. Our approach is inspired by proof theory, and uses a form of update recursion to replace the existence of maximal ideals. Our main result allows us to derive, in a uniform way, algorithms which compute witnesses for existential theorems in countable abstract

We give Hennessy-Milner classes for intuitionistic, dual-intuitionistic and bi-intuitionistic logic interpreted in intuitionistic Kripke models, and generalise these results to modal (dual- and bi-)intuitionistic logics. Our main technical tools are image-compact and pre-image-compact relations that provide a semantical description of modal saturation properties.

This paper focuses on globally sound but possibly locally unsound analytic sequent calculi for quantifier macros defined by sequences of quantifiers. It is demonstrated that no locally sound analytic representation based on the usual eigenvariable condition exists. In consequence, representations by globally sound but possibly locally unsound analytic sequent calculi are used. Cut-elimination is shown

Turing's famous ‘machine’ framework provides an intuitively clear conception of ‘computing with real numbers’. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These counterexamples are often crucial in establishing reversals in the Reverse Mathematics program. All the previous is essentially limited to a language that can only express

Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. More specifically, proposals have been put forward to augment formal semantic machinery with distributional meaning representations, thereby introducing the notion of semantic similarity into formal semantics, or to define distributional systems that aim to incorporate

Logics with team semantics provide alternative means for descriptive characterization of complexity classes. Dependence and independence logic are both known to capture non-deterministic polynomial time, and the frontiers of tractability in these logics are relatively well understood. Inclusion logic is similar to these team-based logical formalisms with the exception that it corresponds to deterministic

Beklemishev introduced an ordinal notation system for the Feferman-Schütte ordinal Γ0 based on the autonomous expansion of provability algebras. In this paper we present the logic BC (for Bracket Calculus). The language of BC extends said ordinal notation system to a strictly positive modal language. Thus, unlike other provability logics, BC is based on a self-contained signature that gives rise to

We introduce proper display calculi for basic monotonic modal logic, the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal applies the multi-type methodology in the design of proper display calculi, starting from a semantic analysis which motivates syntactic translations from

An automaton is unambiguous if for every input it has at most one accepting computation. An automaton is finitely (respectively, countably) ambiguous if for every input it has at most finitely (respectively, countably) many accepting computations. An automaton is boundedly ambiguous if there is k∈N, such that for every input it has at most k accepting computations. We consider nondeterministic Büchi

The problem of matching a query string to a directed graph, whose vertices are labeled by strings, has application in different fields, from data mining to computational biology. Several variants of the problem have been considered, depending on the fact that the match is exact or approximate and, in the approximate case, which edit operations are considered and where they are allowed. In this paper

The suffix tree is a fundamental data structure in stringology, but its space usage, though linear, is an important problem in applications like Bioinformatics. We design and implement a new compressed suffix tree (CST) targeted to highly repetitive texts, such as large genomic collections of the same species. Our first contribution is to enhance the Block Tree, a data structure that captures the repetitiveness

We investigate inference of variable-length codes in other domains of computer science, such as noisy information transmission or information retrieval-storage: in such topics, traditionally mostly constant-length codewords act. The study is relied upon the two concepts of independent and closed sets: given an alphabet A and a binary relation τ⊆A⁎×A⁎, a set X⊆A⁎ is τ-independent if τ(X)∩X=∅; X is τ-closed

A real number x is absolutely normal if, for every base b≥2, every two equally long strings of digits appear with equal asymptotic frequency in the base-b expansion of x. This paper presents an explicit algorithm that generates the binary expansion of an absolutely normal number x, with the nth bit of x appearing after npolylog(n) computation steps. This speed is achieved by simultaneously computing

We investigate systems of equations and the first-order theory of one-relator monoids. We describe a family F of one-relator monoids of the form 〈A|w=1〉 where for each monoid M in F, the longstanding open problem of decidability of word equations with length constraints reduces to the Diophantine problem (i.e. decidability of systems of equations) in M. We achieve this result by finding an interpretation

Schedulability is a fundamental problem in analyzing real-time systems, but it often has to be approximated due to the intrinsic computational hardness. As the most popular polynomial-time and practical algorithm for deciding schedulability on multiprocessor platforms, the speedup factor of Partitioned-EDF is challenging to analyze and is far from being determined. Partitioned-EDF was first proposed

We study the capabilities of probabilistic finite-state machines that act as verifiers for certificates of language membership for input strings, in the regime where the verifiers are restricted to toss some fixed nonzero number of coins regardless of the input size. Say and Yakaryılmaz showed that the class of languages that could be verified by these machines within an error bound strictly less than

A k-threshold function on a rectangular grid of size m×n is the conjunction of k threshold functions on the same domain. In this paper, we focus on the case k=2 and show that the number of two-dimensional 2-threshold functions is 2512π4m4n4+o(m4n4).

In this paper we consider a generalization of the well-known budgeted maximum coverage problem. We are given a ground set of elements and a set of bins. Each bin has its own cost and the cost of each element depends on its associated bin. The goal is to find a subset of elements along with an associated set of bins such that the overall costs of both is at most a given budget, and the profit is maximized

Outsourcing computation has gained significant popularity in recent years due to the prevalence of cloud computing. There are two main security concerns in outsourcing computation: how to guarantee the cloud server performs the computation correctly and how to keep the client's data secret. The single-server verifiable computation (SSVC) of Gennaro, Gentry and Parno (Crypto'10) enables a client to

In the well-known cake cutting problem, a cake needs to be divided among n players who possibly have different valuations for different pieces of the cake. We consider a variation of this problem in which the cake represents chores that need to be allocated. As the players are assumed to be work-averse, this means that each agent now desires to get as little of the cake as possible. In this work, we

We consider the following variant of the mortality problem: given k×k matrices A1,A2,…,At, do there exist t nonnegative integers m1,m2,…,mt such that the product A1m1A2m2⋯Atmt is equal to the zero matrix? It is known that this problem is decidable when t≤2 for matrices over algebraic numbers but becomes undecidable for sufficiently large t and k, even for integral matrices. In this paper, we prove

Given a set P of points in the Euclidean plane and two triangulations of P, the flip distance between these two triangulations is the minimum number of flips required to transform one triangulation into the other. The Parameterized Flip Distance problem is to decide if the flip distance between two given triangulations is equal to a given integer k. The previous best FPT algorithm runs in time O⁎(k⋅ck)

A recently introduced operation of geometrical closure on formal languages is investigated from the viewpoint of the algebraic theory of regular languages. Positive varieties V, for which geometrical closure of every language in V is regular, are fully characterised by the property that V is included in W, a known positive variety arising, e.g., in the study of the commutative closure. It is proved

Automatic sequences can be defined by DFAs with output (DFAO) in two natural ways. We propose to consider the minimal size of a corresponding DFAO as the complexity measure of the automatic sequence, for both variants. This paper compares these complexity measures and investigates their properties, such as the relationships with kernel and morphic sequences. There exist automatic sequences for which

Search trees are commonly used to implement access operations to a set of stored keys. If this set is static and the probabilities of membership queries are known in advance, then one can precompute an optimal search tree, namely one that minimizes the expected access cost. For a non-key query, a search tree can determine its approximate location by returning the inter-key interval containing the query

For one-safe Petri nets or condition/event-systems, a process as defined by Carl Adam Petri provides a notion of a run of a system where causal dependencies are reflected in terms of a partial order. Goltz and Reisig have generalised this concept for nets where places carry multiple tokens, by distinguishing tokens according to their causal history. However, this so-called individual token interpretation

Treasure hunt is finding an inert target by a mobile agent. We consider treasure hunt in polygonal terrains with polygonal obstacles. The agent finds the treasure when there is a segment of length at most 1 between them, inside the terrain. The cost of treasure hunt is the length of the agent's trajectory. We investigate the amount of information (advice complexity) needed for treasure hunt at cost

We develop a behavioural theory for monitors, computational entities that passively analyse the runtime behaviour of systems so as to infer properties about them. First, we present a monitor language and an instrumentation relation used for piCalculus process monitoring. We then identify contextual behavioural preorders that allow us to relate monitors according to criteria defined over monitored executions

We introduce a generalization of An.A.Muchink's non-monotonic betting game, the 1/2-betting game, and show that while there is no single computable 1/2-betting strategy that wins on all Martin-Löf non-random sequences, there is a pair that does.

In the modern era of multi-core systems, the main aim is to utilize the cores properly. This utilization can be done by concurrent programming. But developing a flawless and well-organized concurrent program is difficult. Software Transactional Memory Systems (STMs) are a convenient programming interface which assist the programmer to access the shared memory concurrently without worrying about consistency

We investigate exploration algorithms for autonomous mobile robots evolving in uniform ring-shaped networks. Different from the usual Look-Compute-Move (LCM) model, we consider two characteristics: myopia and luminosity. Myopia means each robot has a limited visibility. We consider the weakest assumption for myopia: each robot can only observe its neighboring nodes. Luminosity means each robot maintains

We consider search in an unknown finite 2D square grid by a metamorphic robotic system consisting of anonymous memory-less modules. Each module autonomously moves while executing a common distributed algorithm and the modules collectively form a robotic system by keeping connectivity. The number of shapes of the metamorphic robotic system grows as the number of modules increases, and a shape of the

We present LB-Spiral, a novel distributed directory protocol for shared objects, suitable for large-scale distributed shared memory systems. Each shared object has an owner node that can modify its value. The ownership may change by moving the object from one node to another in response to move requests. The value of an object can be read by other nodes with lookup requests. The distinctive feature

We consider the fundamental problem of arranging a set of n autonomous robots (points) on a real plane according to an arbitrary given pattern. Each robot operates in a, largely oblivious, look-compute-move step. We measure the time complexity of our algorithms in “epochs,” which denotes the minimum time interval in which every robot performs at least one look-compute-move step. We present a framework

We study the problems of leader election and population size counting for population protocols: networks of finite-state anonymous agents that interact randomly under a uniform random scheduler. We provide simple protocols for approximate counting of the size of the population and for leader election. We show a protocol for leader election that terminates in O(log2⁡nlog⁡m) parallel time, where m is

While a lot of research in distributed computing has covered solutions for self-stabilizing computing and topologies, there is far less work on self-stabilization for distributed data structures. Considering crashing peers in peer-to-peer networks, it should not be taken for granted that a distributed data structure remains intact. In this work, we present a self-stabilizing protocol for a distributed

We consider the state machine replication problem in semi-synchronous systems subject to Byzantine server failures. We propose a new solution to the problem in the form of a protocol for the generalized consensus problem. The protocol solves the consensus problem in a setting in which information about conflicts between transactions is available (such information can be in the form of transaction read

Quantum computation has emerged as a powerful computational medium of our time, having demonstrated the remarkable efficiency in factoring a positive integer and searching databases faster than any currently known classical computing algorithm. Adiabatic evolution of quantum systems have been studied as a potential means that physically realizes quantum computation. Up to now, all the research on adiabatic

Right-one way jumping finite automata are deterministic devices that process their input in a discontinuous fashion. We generalise these devices to nondeterministic machines. More precisely we study the impact on the computational power of these machines when allowing multiple initial states and/or a nondeterministic transition function including spontaneous or λ-transitions. We show inclusion relations

We compute the exact maximum state complexity for the language consisting of m words of length N, and characterize languages achieving the maximum. We also consider a special case, namely languages C(w) consisting of the conjugates of a single word w. The words for which the maximum state complexity of C(w) is achieved turn out to be a natural generalization of de Bruijn words. We show that generalized

Union-free languages are described by regular expressions using only concatenation and Kleene-star. Every regular language can be given as a union of finitely many union-free languages. By the minimal number of union-free languages needed in such union-free decompositions of a regular language, its union-complexity is defined. In this paper, the union-complexity of the languages obtained by various

We introduce the deterministic computational model of an iterated uniform finite-state transducer (iufst). An iufst performs the same length-preserving transduction on several left-to-right sweeps. The first sweep takes place on the input string, while any other sweep processes the output of the previous one. The iufst accepts by halting at the end of a sweep in an accepting state. First, we focus

The paper investigates the state complexity of two operations on regular languages, known as GF(2)-concatenation and GF(2)-inverse of Bakinova et al. (2018) [1], in the case of a one-symbol alphabet. The GF(2)-concatenation is a variant of the classical concatenation obtained by replacing Boolean logic in its definition with the GF(2) field; it is proved that GF(2)-concatenation of two unary languages

In matrix grammars, context-free rules have to be applied in a certain order. However in simple semi-conditional (SSC) grammars, the derivations are controlled either by a permitting string or by a forbidden string associated to each rule. Typical descriptional complexity measures incorporate the number of nonterminals and the number of rules per matrix in a matrix grammar. In SSC grammars, the maximum

Tree width (respectively, string path width) measures the maximal number of partial (respectively, complete) computations of a nondeterministic finite automaton on an input of given length. We characterize polynomial and exponential growth rates of tree width and string path width by structural properties of the corresponding nondeterministic finite automaton (NFA). As the main result we show that

Maximally parallel manner is a usual rule application strategy for P systems, where a maximal set of enabled rules are chosen and each rule in the set is applied as many times as possible. In this work, we consider a rule application strategy, rule synchronization, where some synchronization sets of rules are given, a rule in a synchronization set of rules can be applied only if all rules in the set

In this paper, we propose a novel algorithm to learn a Büchi automaton from a teacher who knows an ω-regular language. The learned Büchi automaton can be a nondeterministic Büchi automaton or a limit deterministic Büchi automaton. The learning algorithm is based on learning a formalism called family of DFAs (FDFAs) recently proposed by Angluin and Fisman. The main catch is that we use a classification

In this paper, we study Reiter's propositional default logic when the treewidth of a certain graph representation (semi-primal graph) of the input theory is bounded. We establish a dynamic programming algorithm on tree decompositions that decides whether a theory has a consistent stable extension ( Cons ). Our algorithm can even be used to enumerate all generating defaults ( EnumSD ) that lead to stable

Reset Petri nets are a particular class of Petri nets where transition firings can remove all tokens from a place without checking if this place actually holds tokens or not. In this paper we look at partial order semantics of reset Petri nets. In particular, we propose a pomset bisimulation for comparing their concurrent behaviours. Building on this pomset bisimulation we then propose a generalization

We investigate the function L(h,p,q), called here the length function, such that L(h,p,q) is the minimum length which guarantees that a natural extension of the periodicity lemma is valid for partial words with h holes and (so-called strong) periods p,q. In a series of papers, the formulae for the length function, in terms of p and q, were provided for each fixed h≤7. We demystify the generic structure

The paper is focused on automata and linear temporal logics for describing the behaviour of real-time pushdown reactive systems. The goal of the paper is to bridge (both in the context of automata and linear temporal logics) tractable formalisms specialized for expressing separately dense-time real-time properties and context-free properties though preserving tractability in the combined setting. As

Variants of the union and concatenation operations on formal languages are investigated, in which Boolean logic in the definitions (that is, conjunction and disjunction) is replaced with the operations in the two-element field GF(2) (conjunction and exclusive OR). Union is thus replaced with symmetric difference, whereas concatenation gives rise to a new GF(2)-concatenation operation, which is notable

The learners considered in this paper process an infinite text of data containing all members of the set to be learnt in cycles, one word in each cycle, and maintain as a long term memory a string which provides all internal data the learner can use in the next cycle. Updating of these strings is usually done by either recursive or automatic learners. The present work looks at transduced learners,

Graph-walking automata (GWA) are finite-state devices that traverse graphs given as an input by following their edges; they have been studied both as a theoretical notion and as a model of pathfinding in robotics. If a graph is regarded as the set of memory configurations of a certain abstract machine, then various families of devices can be described as GWA: such are two-way finite automata, their

A Two-Party Authenticated Key Agreement (2-PAKA) protocol facilitates two communicating entities to equally contribute to the establishment of a shared session key. IDentity-based 2-PAKA (ID-2-PAKA) protocols are widely researched, since it eliminates the need for explicit public-key verification using digital certificates. Over the years, ID-2-PAKA protocols with perfect forward secrecy and Key Generation

In this work, we present the first secure stegosystem in the common computational model which, for any communication channel, is provably secure, reliable, and has nearly optimal bandwidth, but needs super-polynomial time. This solves several open problems about secret-key steganography in the computational model. In particular, our result answers affirmatively the question whether there exists a secure

We formalize and examine the online Dictionary Recognition with One Gap problem (DROG) which is the following. Preprocess a dictionary D of d patterns each containing a special gap symbol that matches any string, so that given a text arriving online a character at a time, all patterns from D which are suffixes of the text that has arrived so far and have not been reported yet, are reported before the