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Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared towards solving and modeling…
Reductions combine collections of inputs with an associative (and here, also commutative) operator to produce collections of outputs. When the same value contributes to multiple outputs, there is an opportunity to reuse partial results,…
A two-dimensional automaton operates on arrays of symbols. While a standard (four-way) two-dimensional automaton can move its input head in four directions, restricted two-dimensional automata are only permitted to move their input heads in…
This thesis is focused on techniques for finite automata and their use in practice, with the main emphasis on nondeterministic tree automata. This concerns namely techniques for size reduction and language inclusion testing, which are two…
Consider nondeterministic finite automata recognizing base-k positional notation of numbers. Assume that numbers are read starting from their least significant digits. It is proved that if two sets of numbers S and T are represented by…
Action description languages, such as A and B, are expressive instruments introduced for formalizing planning domains and planning problem instances. The paper starts by proposing a methodology to encode an action language (with conditional…
A generalization of the max-plus transformation, which is known as a method to derive cellular automata from integrable equations, is proposed for complex numbers. Operation rules for this transformation is also studied for general number…
Cut-elimination is the bedrock of proof theory with a multitude of applications from computational interpretations to proof analysis. It is also the starting point for important meta-theoretical investigations including decidability,…
We introduce a certain restriction of weighted automata over the rationals, called image-binary automata. We show that such automata accept the regular languages, can be exponentially more succinct than corresponding NFAs, and allow for…
Linear Temporal Logic (LTL) is a widely used specification framework for linear time properties of systems. The standard approach for verifying such properties is by transforming LTL formulae to suitable $\omega$-automata and then applying…
Several abstract machines that operate on symbolic input alphabets have been proposed in the last decade, for example, symbolic automata or lattice automata. Applications of these types of automata include software security analysis and…
A "numerical set-expression" is a term specifying a cascade of arithmetic and logical operations to be performed on sets of non-negative integers. If these operations are confined to the usual Boolean operations together with the result of…
This paper presents compact notations for concentration inequalities and convenient results to streamline probabilistic analysis. The new expressions describe the typical sizes and tails of random variables, allowing for simple operations…
It is known that there are no more Lyndon words of length n than there are periodic necklaces of same length. This paper considers a similar problem where, additionally, the necklaces must be without some forbidden factors. This problem…
Finite-state tree automata are a well studied formalism for representing term languages. This paper studies the problem of determining the regularity of the set of instances of a finite set of terms with variables, where each variable is…
We study the relation between the standard two-way automata and more powerful devices, namely, two-way finite automata with an additional "pebble" movable along the input tape. Similarly as in the case of the classical two-way machines, it…
Ordered binary decision diagrams (OBDDs) are a fundamental data structure for the manipulation of Boolean functions, with strong applications to finite-state symbolic model checking. OBDDs allow for efficient algorithms using top-down…
We study the complexity of algorithmic problems for matrices that are represented by multi-terminal decision diagrams (MTDD). These are a variant of ordered decision diagrams, where the terminal nodes are labeled with arbitrary elements of…
We introduce a generic extension of the popular branching-time logic CTL which refines the temporal until and release operators with formal languages. For instance, a language may determine the moments along a path that an until property…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…