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We show that there is an effectively given zero-sum-free commutative semiring S, contained as the subsemiring of nonnegative elements in an effectively given commutative ordered ring, for which there are no procedures deciding, given a weighted ...

• We construct an effectively given zero-sum-free commutative semiring S as a subsemiring of a commutative ordered ring.
• It is undecidable, given a weighted finite automaton over S, whether its support is the language of all words.
• ...

GF(2)-operations on formal languages (Bakinova et al., “Formal languages over GF(2)”, Inf. Comput., 2022) are variants of the classical concatenation and Kleene star obtained by replacing Boolean logic in their definitions with the GF(2) field. ...

• Two operations on formal languages, GF(2)-concatenation and GF(2)-star, are investigated.
• The language family recognized by permutation automata is closed under GF(2)-concatenation, but not under GF(2)-star.
• The language families ...

For the given non-unary input alphabet Σ, a maximal prefix code h mapping strings over Σ to binary strings, and an optimal deterministic finite automaton (DFA) A with n states recognizing a language L over Σ, we consider the problem of how many ...

Given a deterministic finite automaton (DFA) A, we present a simple algorithm for constructing four deterministic finite automata that accept the shortest forbidden factors, the shortest forbidden suffixes, the shortest allowed suffixes, and the ...

We present a weight measure on formal languages based on the summands of a geometric series discounted by the fraction of words of certain length in the language, guaranteeing the weight to be a real value between 0 and 1 for any language. We ...

For a finite permutation group on n elements we show the following (and variants thereof) equivalences: (1) the permutation group is primitive, (2) in the transformation monoid generated by the group and any rank n − 1 mapping there exists, for ...

Two strings are Simon's ∼ k-congruent if they have the same set of subsequences of length at most k. We study Simon's congruence closure of a string, which is regular by definition. Given a string w over an alphabet Σ, we present two ...

Opacity is an important system-theoretic property expressing whether a system may reveal its secret to a passive observer (an intruder) who knows the structure of the system but has only limited observations of its behavior. Several ...

We make progress on a generalization of the road (colouring) problem. The road problem was posed by Adler-Goodwyn-Weiss and solved by Trahtman. The generalization was posed, and solved in certain special cases, by Ashley-Marcus-Tuncel. ...

Computational complexity theory is the study of the fundamental resource requirements associated with the solutions of different problems. Time, space (memory) and randomness (number of coin tosses) are some of the resource types that have been ...

Case split is a core proof rule in current decision procedures for the theory of string constraints. Its use is the primary cause of the state space explosion in string constraint solving, since it is the only rule that creates branches in the ...

• Solving string constraints using regular model checking.
• Nielsen transformation using automata and transducers.
• Compact encoding of the generated state space.
• Provides significant advantage on hard formulae.

Given an order of the underlying alphabet, we can lift it to the states of a finite deterministic automaton: to compare states we use the order of the strings reaching them. When the order on strings is the co-lexicographic one and ...

• The best possible encodings (compression) of DFAs and NFAs are obtained by imposing a suitable order on their states.

Graph-walking automata (GWA) traverse graphs by moving between the nodes following the edges, using a finite-state control to decide where to go next. It is known that every GWA can be transformed to a GWA that halts on every input, to ...

Watson–Crick (WK) finite automata are working on a Watson–Crick tape, that is, on an abstract construct similar to DNA molecules. Therefore, it has two reading heads. While in traditional WK automata both heads read the whole input in the same ...${\mathrm{}}^{}{\mathrm{}}^{}$${\mathrm{}}^{}{\mathrm{}}^{}$

Diagnosability of a discrete event system is usually dealt at the system level entailing synchronous composition of component automata leading to state explosion problem. However, many of the systems are modular in nature allowing localized ...

Operations on regular languages that commute with any inverse alphabetic morphism are called 1-uniform transformations. In a previous work we have shown that these operations are encoded by operations on automata, called modifiers, ...

Nonuniform families of polynomial-size finite automata, which are series of indexed finite automata having polynomially many inner states, are used in the past literature to solve nonuniform families of promise decision problems. In such a ...

We provide algorithmic methods for connected reconfiguration of lattice-based cellular structures by finite-state robots, motivated by large-scale constructions in space. We present algorithms that are able to detect and reconfigure arbitrary ...

Nondeterministic finite automata (NFAs) are an important model of computation. The equivalence problem for NFAs is known to be PSPACE-complete, and several specialized algorithms have been developed to solve this problem. In this paper, we ...

Two strings are Simon’s ${\sim }_k$-congruent if they have the same set of subsequences of length at most k. We study the Simon’s congruence closure of a string, which is regular by definition. Given a string w over an alphabet $\Sigma$, we present an efficient ...${}_{}$$$${}_{}$