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Paulo Mateus

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Papers by Paulo Mateus

Decidability of the Equivalence of Multi-Letter Quantum Finite Automata

arXiv (Cornell University), Dec 5, 2008

Multi-letter quantum finite automata (QFAs) were a quantum variant of classical oneway multi-head... more Multi-letter quantum finite automata (QFAs) were a quantum variant of classical oneway multi-head finite automata (J. Hromkovič, Acta Informatica 19 (1983) 377-384), and it has been shown that this new one-way QFAs (multi-letter QFAs) can accept with no error some regular languages (a + b) * b that are unacceptable by the previous one-way QFAs. In this paper, we study the decidability of the equivalence of multi-letter QFAs, and the main technical contributions are as follows: (1) We show that any two automata, a k 1-letter QFA A 1 and a k 2-letter QFA A 2 , over the same input alphabet Σ are equivalent if and only if they are (n 2 m k−1 − m k−1 + k)-equivalent, where m = |Σ| is the cardinality of Σ, k = max(k 1 , k 2), and n = n 1 + n 2 , with n 1 and n 2 being the numbers of states of A 1 and A 2 , respectively. When k = 1, we obtain the decidability of equivalence of measure-once QFAs in the literature. It is worth mentioning that our technical method is essentially different from that for the decidability of the case of single input alphabet (i.e., m = 1). (2) However, if we determine the equivalence of multi-letter QFAs by checking all strings of length not more than n 2 m k−1 − m k−1 + k, then the worst time complexity is exponential, i.e., O(n 6 m n 2 m k−1 −m k−1 +2k−1). Therefore, we design a polynomial-time O(m 2k−1 n 8 + km k n 6) algorithm for determining the equivalence of any two multi-letter QFAs. Here, the time complexity is concerning the number of states in the multi-letter QFAs, and k is thought of as a constant.

A Private Quantum Bit String Commitment

Entropy, 2020

We propose an entanglement-based quantum bit string commitment protocol whose composability is pr... more We propose an entanglement-based quantum bit string commitment protocol whose composability is proven in the random oracle model. This protocol has the additional property of preserving the privacy of the committed message. Even though this property is not resilient against man-in-the-middle attacks, this threat can be circumvented by considering that the parties communicate through an authenticated channel. The protocol remains secure and private (but not composable) if we realize the random oracles as physical unclonable functions (PUFs) in the so-called bad PUF model.

Decidability of Approximate Skolem Problem and Applications to Logical Verification of Dynamical Properties of Markov Chains

ACM Transactions on Computational Logic, 2015

When studying probabilistic dynamical systems, temporal logic has typically been used to analyze ... more When studying probabilistic dynamical systems, temporal logic has typically been used to analyze path properties. Recently, there has been some interest in analyzing the dynamical evolution of state probabilities of these systems. In this article, we show that verifying linear temporal properties concerning the state evolution induced by a Markov chain is equivalent to the decidability of the Skolem problem -- a long-standing open problem in Number Theory. However, from a practical point of view, usually it is enough to check properties up to some acceptable error bound ϵ. We show that an approximate version of the Skolem problem is decidable, and that it can be applied to verify, up to arbitrarily small ϵ, linear temporal properties of the state evolution induced by a Markov chain.

Secure N-dimensional simultaneous dense coding and applications

International Journal of Quantum Information, 2015

Simultaneous dense coding (SDC) guarantees that Bob and Charlie simultaneously receive their resp... more Simultaneous dense coding (SDC) guarantees that Bob and Charlie simultaneously receive their respective information from Alice in their respective processes of dense coding. The idea is to use the so-called locking operation to “lock” the entanglement channels, thus requiring a joint unlocking operation by Bob and Charlie in order to simultaneously obtain the information sent by Alice. We present some new results on SDC: (1) We propose three SDC protocols, which use different N-dimensional entanglement (Bell state, W state and GHZ state). (2) Besides the quantum Fourier transform, two new locking operators are introduced (the double controlled-NOT operator and the SWAP operator). (3) In the case that spatially distant Bob and Charlie have to finalize the protocol by implementing the unlocking operation through communication, we improve our protocol’s fairness, with respect to Bob and Charlie, by implementing the unlocking operation in series of steps. (4) We improve the security of ...

Reasoning About States of Probabilistic Sequential Programs

Lecture Notes in Computer Science, 2006

A complete and decidable propositional logic for reasoning about states of probabilistic sequenti... more A complete and decidable propositional logic for reasoning about states of probabilistic sequential programs is presented. The state logic is then used to obtain a sound Hoare-style calculus for basic probabilistic sequential programs. The Hoare calculus presented herein is the first probabilistic Hoare calculus with a complete and decidable state logic that has truth-functional propositional (not arithmetical) connectives. The models of the state logic are obtained exogenously by attaching sub-probability measures to valuations over memory cells. In order to achieve complete and recursive axiomatization of the state logic, the probabilities are taken in arbitrary real closed fields.

Quantum blind signature with an offline repository

International Journal of Quantum Information, 2015

We propose a quantum blind signature scheme that achieves perfect security under the assumption o... more We propose a quantum blind signature scheme that achieves perfect security under the assumption of an honest offline repository. The security of the protocol also relies on perfect private quantum channels, which are achievable using quantum one-time pads with keys shared via a quantum key distribution (QKD) protocol. The proposed approach ensures that signatures cannot be copied and that the sender must compromise to a single message, which are important advantages over classical protocols for certain applications.

Realization of Probabilistic Automata: Categorical Approach

Lecture Notes in Computer Science, 2000

We present a categorical framework to study probabilistic automata starting by obtaining aggregat... more We present a categorical framework to study probabilistic automata starting by obtaining aggregation and interconnection as universal constructions. We also introduce the notion of probabilistic behavior in order to get adjunctions between probabilistic behavior and probabilistic automata. Thus we are able to extend to the probabilistic setting free and minimal realizations as universal constructions. * f (x) f (s) (ω).

Combining Logics: Parchments Revisited

Lecture Notes in Computer Science, 2002

Towards model-checking quantum security protocols

First International Conference on Quantum, Nano, and Micro Technologies, ICQNM 2007, 2007

Logics for reasoning about quantum states have been given in the literature. In this paper, we ex... more Logics for reasoning about quantum states have been given in the literature. In this paper, we extend one such logic with temporal constructs mimicking the standard computational tree logic used to reason about classical transition systems. We investigate the model-checking problem for this temporal quantum logic and illustrate its use by reasoning about the BB84 key distribution protocol.

Exponentially more concise quantum recognition of non-RMM regular languages

We show that there are quantum devices that accept all regular languages and that are exponential... more We show that there are quantum devices that accept all regular languages and that are exponentially more concise than deterministic finite automata (DFA). For this purpose, we introduce a new computing model of one-way quantum finite automata (1QFA), namely, one-way quantum finite automata together with classical states (1QFAC), which extends naturally both measure-only 1QFA and DFA and whose state complexity is upperbounded by both. The original contributions of the paper are the following. First, we show that the set of languages accepted by 1QFAC with bounded error consists precisely of all regular languages. Second, we prove that 1QFAC are at most exponentially more concise than DFA. Third, we show that the previous bound is tight for families of regular languages that are not recognized by measure-once (RMO), measure-many (RMM) and multi-letter 1QFA. Fourth, we give a polynomial-time algorithm for determining whether any two 1QFAC are equivalent. Finally, we show that state minimization of 1QFAC is decidable within EXPSPACE. We conclude the paper by posing some open problems.

Characterizations of one-way general quantum finite automata

Theoretical Computer Science, 2012

Generally, unitary transformations limit the computational power of quantum finite automata (QFA)... more Generally, unitary transformations limit the computational power of quantum finite automata (QFA). In this paper we study a generalized model named one-way general quantum finite automata (1gQFA), in which each symbol in the input alphabet induces a trace-preserving quantum operation, instead of a unitary transformation. Two different kinds of 1gQFA will be studied: measureonce one-way general quantum finite automata (MO-1gQFA) where a measurement deciding to accept or reject is performed at the end of a computation, and measure-many one-way general quantum finite automata (MM-1gQFA) where a similar measurement is performed after each trace-preserving quantum operation on reading each input symbol. We characterize the measure-once model from three aspects: the closure property, the language recognition power, and the equivalence problem. Specially, we prove that MO-1gQFA recognize, with bounded error, precisely the set of all regular languages. Our results imply that some quantum finite automata proposed in the literature, which were expected to be more powerful, still can not recognize non-regular languages.

A brief review on quantum bit commitment

Second International Conference on Applications of Optics and Photonics, 2014

In classical cryptography, the bit commitment scheme is one of the most important primitives. We ... more In classical cryptography, the bit commitment scheme is one of the most important primitives. We review the state of the art of bit commitment protocols, emphasizing its main achievements and applications. Next, we present a practical quantum bit commitment scheme, whose security relies on current technological limitations, such as the lack of long-term stable quantum memories. We demonstrate the feasibility of our practical quantum bit commitment protocol and that it can be securely implemented with nowadays technology.

Decidability and complexity for -regular properties of stochastic systems

Logic Journal of IGPL, 2012

Herein we study the probabilization of Quantified Linear Temporal Logic, which we call PQLTL. PQL... more Herein we study the probabilization of Quantified Linear Temporal Logic, which we call PQLTL. PQLTL can reason about any semialgebraic constrain over probabilities of paths of a Markov chain satisfying a QLTL formulae. PQLTL is related with other commonly used probabilistic temporal logics (such as PLTL, PCTL and PCTL *) that were devised only to specify properties for which model checking algorithms are amenable and whose basic results, such as completeness and decidability, were never investigated. In this paper, we devise a strong and a weak SAT algorithm for PQLTL. The former relies in [n+2]-EXPSPACE and the latter in [n+1]-EXPSPACE where n is the alternation depth of the quantifiers in the input formula. The weak SAT algorithm for the existential fragment, which has all the expressive power of PQLTL, is in EXPSPACE. Another relevant fragment of PQLTL is the linear closure of PCTL * without nesting of the probability operator. We show that the SAT problem for this fragment is PSPACE complete. Capitalizing in these results, we derive a complete calculus for PQLTL and illustrate it with a toy example.

Quantum secret sharing with classical Bobs

Journal of Physics A: Mathematical and Theoretical, 2013

Boyer, Kenigsberg, and Mor [Phys.Rev.Lett.99, 140501(2007)] proposed a novel idea of semi-quantum... more Boyer, Kenigsberg, and Mor [Phys.Rev.Lett.99, 140501(2007)] proposed a novel idea of semi-quantum key distribution where a key can be securely distributed between Alice who can perform any quantum operation and Bob who is classical. Extending the idea of "semiquantum" to other tasks of quantum information processing is of interest and worth considering. In this article, we consider the issue of semi-quantum secret sharing where a quantum participant Alice can share a secret key with two classical participants Bobs. After analyzing the existing protocol, we propose a new protocol of semi-quantum secret sharing. Our protocol is more realistic, since it utilizes product states instead of entangled states. We prove that any attempt of an adversary to obtain information necessarily induces some errors that the legitimate users could notice.

Non-Determinism and Uncertainty in the Situation Calculus

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2000

The purpose of this article is to extend the situation calculus, a logical framework for the spec... more The purpose of this article is to extend the situation calculus, a logical framework for the specification of theories of action and change, with actions that have a non-deterministic or uncertain nature. Our approach is based upon the idea that actions may have a deterministic component, and a probabilistic component. For example, the act of flipping a coin has a deterministic component (the actual coin toss) and an uncertain component (the outcome). We extend the language of the situation calculus in order to make explicit this distinction between these two action components. Furthermore, we provide means to reason about the outcomes of processes specified only in terms of deterministic action components (which we call behaviors). In particular, we show how one can compute the probability that some fluent will hold after specific behavior is realized. An important feature of our approach is that the syntactic and semantic structure of actions and situations is independent of the d...

Security Analyses and Improvement of Arbitrated Quantum Signature with an Untrusted Arbitrator

International Journal of Theoretical Physics, 2013

Very recently, an arbitrated quantum signature (AQS) scheme of classical message with an untruste... more Very recently, an arbitrated quantum signature (AQS) scheme of classical message with an untrusted arbitrator was presented[Eur. Phys. J. D 61(3), 773 (2011)]. In this paper, the security of the AQS scheme with an untrusted arbitrator is analyzed. An AQS scheme with an untrusted arbitrator should satisfy the unforgeable property and undeniable property. In particular, the malicious verifier can not modify a message and its signature to produce a new message with a valid signature, and the dishonest signer who really has sent the message to the verifier which the verifier accepted as an authentic one cannot later deny having sent this message. However, we show that, in the AQS scheme with an untrusted arbitrator, the dishonest signer can successfully disavow his/her signature and the malicious verifier can counterfeit a valued signature for any message by known message attack when he has received a message-signature pair. Then, we suggest an improved AQS scheme of classical message with an untrusted arbitrator that can solve effectively the two problems raised above. Finally, we prove the security of the improved scheme.

On the complexity of minimizing probabilistic and quantum automata

Information and Computation, 2012

Several types of automata, such as probabilistic and quantum automata, require to work with real ... more Several types of automata, such as probabilistic and quantum automata, require to work with real and complex numbers. For such automata the acceptance of an input is quantified with a probability. There are plenty of results in the literature addressing the complexity of checking the equivalence of these automata, that is, checking whether two automata accept all inputs with the same probability. On the other hand, the critical problem of finding the minimal automata equivalent to a given one has been left open (C. Moore, J.P. Crutchfield, Theoretical Computer Science 237 (2000) 275-306, p. 304, Problem 5). In this work, we reduce the minimization problem of probabilistic and quantum automata to finding a solution of a system of algebraic polynomial (in)equations. An EXPSPACE upper bound on the complexity of the minimization problem is derived by applying Renegar's algorithm. More specifically, we show that the state minimization of probabilistic automata, measure-once quantum automata, measure-many quantum automata, measure-once generalized quantum automata, and measure-many generalized quantum automata is decidable and in EXPSPACE. Finally, we also solve an open problem concerning minimal covering of stochastic sequential machines (A. Paz, Introduction to Probabilistic Automata, Academic Press, 1971, Page 43).

Decidability of the Equivalence of Multi-Letter Quantum Finite Automata

arXiv (Cornell University), Dec 5, 2008

Multi-letter quantum finite automata (QFAs) were a quantum variant of classical oneway multi-head... more Multi-letter quantum finite automata (QFAs) were a quantum variant of classical oneway multi-head finite automata (J. Hromkovič, Acta Informatica 19 (1983) 377-384), and it has been shown that this new one-way QFAs (multi-letter QFAs) can accept with no error some regular languages (a + b) * b that are unacceptable by the previous one-way QFAs. In this paper, we study the decidability of the equivalence of multi-letter QFAs, and the main technical contributions are as follows: (1) We show that any two automata, a k 1-letter QFA A 1 and a k 2-letter QFA A 2 , over the same input alphabet Σ are equivalent if and only if they are (n 2 m k−1 − m k−1 + k)-equivalent, where m = |Σ| is the cardinality of Σ, k = max(k 1 , k 2), and n = n 1 + n 2 , with n 1 and n 2 being the numbers of states of A 1 and A 2 , respectively. When k = 1, we obtain the decidability of equivalence of measure-once QFAs in the literature. It is worth mentioning that our technical method is essentially different from that for the decidability of the case of single input alphabet (i.e., m = 1). (2) However, if we determine the equivalence of multi-letter QFAs by checking all strings of length not more than n 2 m k−1 − m k−1 + k, then the worst time complexity is exponential, i.e., O(n 6 m n 2 m k−1 −m k−1 +2k−1). Therefore, we design a polynomial-time O(m 2k−1 n 8 + km k n 6) algorithm for determining the equivalence of any two multi-letter QFAs. Here, the time complexity is concerning the number of states in the multi-letter QFAs, and k is thought of as a constant.

A Private Quantum Bit String Commitment

Entropy, 2020

We propose an entanglement-based quantum bit string commitment protocol whose composability is pr... more We propose an entanglement-based quantum bit string commitment protocol whose composability is proven in the random oracle model. This protocol has the additional property of preserving the privacy of the committed message. Even though this property is not resilient against man-in-the-middle attacks, this threat can be circumvented by considering that the parties communicate through an authenticated channel. The protocol remains secure and private (but not composable) if we realize the random oracles as physical unclonable functions (PUFs) in the so-called bad PUF model.

Decidability of Approximate Skolem Problem and Applications to Logical Verification of Dynamical Properties of Markov Chains

ACM Transactions on Computational Logic, 2015

When studying probabilistic dynamical systems, temporal logic has typically been used to analyze ... more When studying probabilistic dynamical systems, temporal logic has typically been used to analyze path properties. Recently, there has been some interest in analyzing the dynamical evolution of state probabilities of these systems. In this article, we show that verifying linear temporal properties concerning the state evolution induced by a Markov chain is equivalent to the decidability of the Skolem problem -- a long-standing open problem in Number Theory. However, from a practical point of view, usually it is enough to check properties up to some acceptable error bound ϵ. We show that an approximate version of the Skolem problem is decidable, and that it can be applied to verify, up to arbitrarily small ϵ, linear temporal properties of the state evolution induced by a Markov chain.

Secure N-dimensional simultaneous dense coding and applications

International Journal of Quantum Information, 2015

Simultaneous dense coding (SDC) guarantees that Bob and Charlie simultaneously receive their resp... more Simultaneous dense coding (SDC) guarantees that Bob and Charlie simultaneously receive their respective information from Alice in their respective processes of dense coding. The idea is to use the so-called locking operation to “lock” the entanglement channels, thus requiring a joint unlocking operation by Bob and Charlie in order to simultaneously obtain the information sent by Alice. We present some new results on SDC: (1) We propose three SDC protocols, which use different N-dimensional entanglement (Bell state, W state and GHZ state). (2) Besides the quantum Fourier transform, two new locking operators are introduced (the double controlled-NOT operator and the SWAP operator). (3) In the case that spatially distant Bob and Charlie have to finalize the protocol by implementing the unlocking operation through communication, we improve our protocol’s fairness, with respect to Bob and Charlie, by implementing the unlocking operation in series of steps. (4) We improve the security of ...

Reasoning About States of Probabilistic Sequential Programs

Lecture Notes in Computer Science, 2006

A complete and decidable propositional logic for reasoning about states of probabilistic sequenti... more A complete and decidable propositional logic for reasoning about states of probabilistic sequential programs is presented. The state logic is then used to obtain a sound Hoare-style calculus for basic probabilistic sequential programs. The Hoare calculus presented herein is the first probabilistic Hoare calculus with a complete and decidable state logic that has truth-functional propositional (not arithmetical) connectives. The models of the state logic are obtained exogenously by attaching sub-probability measures to valuations over memory cells. In order to achieve complete and recursive axiomatization of the state logic, the probabilities are taken in arbitrary real closed fields.

Quantum blind signature with an offline repository

International Journal of Quantum Information, 2015

We propose a quantum blind signature scheme that achieves perfect security under the assumption o... more We propose a quantum blind signature scheme that achieves perfect security under the assumption of an honest offline repository. The security of the protocol also relies on perfect private quantum channels, which are achievable using quantum one-time pads with keys shared via a quantum key distribution (QKD) protocol. The proposed approach ensures that signatures cannot be copied and that the sender must compromise to a single message, which are important advantages over classical protocols for certain applications.

Realization of Probabilistic Automata: Categorical Approach

Lecture Notes in Computer Science, 2000

We present a categorical framework to study probabilistic automata starting by obtaining aggregat... more We present a categorical framework to study probabilistic automata starting by obtaining aggregation and interconnection as universal constructions. We also introduce the notion of probabilistic behavior in order to get adjunctions between probabilistic behavior and probabilistic automata. Thus we are able to extend to the probabilistic setting free and minimal realizations as universal constructions. * f (x) f (s) (ω).

Combining Logics: Parchments Revisited

Lecture Notes in Computer Science, 2002

Towards model-checking quantum security protocols

First International Conference on Quantum, Nano, and Micro Technologies, ICQNM 2007, 2007

Logics for reasoning about quantum states have been given in the literature. In this paper, we ex... more Logics for reasoning about quantum states have been given in the literature. In this paper, we extend one such logic with temporal constructs mimicking the standard computational tree logic used to reason about classical transition systems. We investigate the model-checking problem for this temporal quantum logic and illustrate its use by reasoning about the BB84 key distribution protocol.

Exponentially more concise quantum recognition of non-RMM regular languages

We show that there are quantum devices that accept all regular languages and that are exponential... more We show that there are quantum devices that accept all regular languages and that are exponentially more concise than deterministic finite automata (DFA). For this purpose, we introduce a new computing model of one-way quantum finite automata (1QFA), namely, one-way quantum finite automata together with classical states (1QFAC), which extends naturally both measure-only 1QFA and DFA and whose state complexity is upperbounded by both. The original contributions of the paper are the following. First, we show that the set of languages accepted by 1QFAC with bounded error consists precisely of all regular languages. Second, we prove that 1QFAC are at most exponentially more concise than DFA. Third, we show that the previous bound is tight for families of regular languages that are not recognized by measure-once (RMO), measure-many (RMM) and multi-letter 1QFA. Fourth, we give a polynomial-time algorithm for determining whether any two 1QFAC are equivalent. Finally, we show that state minimization of 1QFAC is decidable within EXPSPACE. We conclude the paper by posing some open problems.

Characterizations of one-way general quantum finite automata

Theoretical Computer Science, 2012

Generally, unitary transformations limit the computational power of quantum finite automata (QFA)... more Generally, unitary transformations limit the computational power of quantum finite automata (QFA). In this paper we study a generalized model named one-way general quantum finite automata (1gQFA), in which each symbol in the input alphabet induces a trace-preserving quantum operation, instead of a unitary transformation. Two different kinds of 1gQFA will be studied: measureonce one-way general quantum finite automata (MO-1gQFA) where a measurement deciding to accept or reject is performed at the end of a computation, and measure-many one-way general quantum finite automata (MM-1gQFA) where a similar measurement is performed after each trace-preserving quantum operation on reading each input symbol. We characterize the measure-once model from three aspects: the closure property, the language recognition power, and the equivalence problem. Specially, we prove that MO-1gQFA recognize, with bounded error, precisely the set of all regular languages. Our results imply that some quantum finite automata proposed in the literature, which were expected to be more powerful, still can not recognize non-regular languages.

A brief review on quantum bit commitment

Second International Conference on Applications of Optics and Photonics, 2014

In classical cryptography, the bit commitment scheme is one of the most important primitives. We ... more In classical cryptography, the bit commitment scheme is one of the most important primitives. We review the state of the art of bit commitment protocols, emphasizing its main achievements and applications. Next, we present a practical quantum bit commitment scheme, whose security relies on current technological limitations, such as the lack of long-term stable quantum memories. We demonstrate the feasibility of our practical quantum bit commitment protocol and that it can be securely implemented with nowadays technology.

Decidability and complexity for -regular properties of stochastic systems

Logic Journal of IGPL, 2012

Herein we study the probabilization of Quantified Linear Temporal Logic, which we call PQLTL. PQL... more Herein we study the probabilization of Quantified Linear Temporal Logic, which we call PQLTL. PQLTL can reason about any semialgebraic constrain over probabilities of paths of a Markov chain satisfying a QLTL formulae. PQLTL is related with other commonly used probabilistic temporal logics (such as PLTL, PCTL and PCTL *) that were devised only to specify properties for which model checking algorithms are amenable and whose basic results, such as completeness and decidability, were never investigated. In this paper, we devise a strong and a weak SAT algorithm for PQLTL. The former relies in [n+2]-EXPSPACE and the latter in [n+1]-EXPSPACE where n is the alternation depth of the quantifiers in the input formula. The weak SAT algorithm for the existential fragment, which has all the expressive power of PQLTL, is in EXPSPACE. Another relevant fragment of PQLTL is the linear closure of PCTL * without nesting of the probability operator. We show that the SAT problem for this fragment is PSPACE complete. Capitalizing in these results, we derive a complete calculus for PQLTL and illustrate it with a toy example.

Quantum secret sharing with classical Bobs

Journal of Physics A: Mathematical and Theoretical, 2013

Boyer, Kenigsberg, and Mor [Phys.Rev.Lett.99, 140501(2007)] proposed a novel idea of semi-quantum... more Boyer, Kenigsberg, and Mor [Phys.Rev.Lett.99, 140501(2007)] proposed a novel idea of semi-quantum key distribution where a key can be securely distributed between Alice who can perform any quantum operation and Bob who is classical. Extending the idea of "semiquantum" to other tasks of quantum information processing is of interest and worth considering. In this article, we consider the issue of semi-quantum secret sharing where a quantum participant Alice can share a secret key with two classical participants Bobs. After analyzing the existing protocol, we propose a new protocol of semi-quantum secret sharing. Our protocol is more realistic, since it utilizes product states instead of entangled states. We prove that any attempt of an adversary to obtain information necessarily induces some errors that the legitimate users could notice.

Non-Determinism and Uncertainty in the Situation Calculus

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2000

The purpose of this article is to extend the situation calculus, a logical framework for the spec... more The purpose of this article is to extend the situation calculus, a logical framework for the specification of theories of action and change, with actions that have a non-deterministic or uncertain nature. Our approach is based upon the idea that actions may have a deterministic component, and a probabilistic component. For example, the act of flipping a coin has a deterministic component (the actual coin toss) and an uncertain component (the outcome). We extend the language of the situation calculus in order to make explicit this distinction between these two action components. Furthermore, we provide means to reason about the outcomes of processes specified only in terms of deterministic action components (which we call behaviors). In particular, we show how one can compute the probability that some fluent will hold after specific behavior is realized. An important feature of our approach is that the syntactic and semantic structure of actions and situations is independent of the d...

Security Analyses and Improvement of Arbitrated Quantum Signature with an Untrusted Arbitrator

International Journal of Theoretical Physics, 2013

Very recently, an arbitrated quantum signature (AQS) scheme of classical message with an untruste... more Very recently, an arbitrated quantum signature (AQS) scheme of classical message with an untrusted arbitrator was presented[Eur. Phys. J. D 61(3), 773 (2011)]. In this paper, the security of the AQS scheme with an untrusted arbitrator is analyzed. An AQS scheme with an untrusted arbitrator should satisfy the unforgeable property and undeniable property. In particular, the malicious verifier can not modify a message and its signature to produce a new message with a valid signature, and the dishonest signer who really has sent the message to the verifier which the verifier accepted as an authentic one cannot later deny having sent this message. However, we show that, in the AQS scheme with an untrusted arbitrator, the dishonest signer can successfully disavow his/her signature and the malicious verifier can counterfeit a valued signature for any message by known message attack when he has received a message-signature pair. Then, we suggest an improved AQS scheme of classical message with an untrusted arbitrator that can solve effectively the two problems raised above. Finally, we prove the security of the improved scheme.

On the complexity of minimizing probabilistic and quantum automata

Information and Computation, 2012

Several types of automata, such as probabilistic and quantum automata, require to work with real ... more Several types of automata, such as probabilistic and quantum automata, require to work with real and complex numbers. For such automata the acceptance of an input is quantified with a probability. There are plenty of results in the literature addressing the complexity of checking the equivalence of these automata, that is, checking whether two automata accept all inputs with the same probability. On the other hand, the critical problem of finding the minimal automata equivalent to a given one has been left open (C. Moore, J.P. Crutchfield, Theoretical Computer Science 237 (2000) 275-306, p. 304, Problem 5). In this work, we reduce the minimization problem of probabilistic and quantum automata to finding a solution of a system of algebraic polynomial (in)equations. An EXPSPACE upper bound on the complexity of the minimization problem is derived by applying Renegar's algorithm. More specifically, we show that the state minimization of probabilistic automata, measure-once quantum automata, measure-many quantum automata, measure-once generalized quantum automata, and measure-many generalized quantum automata is decidable and in EXPSPACE. Finally, we also solve an open problem concerning minimal covering of stochastic sequential machines (A. Paz, Introduction to Probabilistic Automata, Academic Press, 1971, Page 43).