*359The petitioner, Danny Brown, known also as Daniel Brown,1 appeals following the denial of his *360petition for certification to appeal from the judgment of the habeas court denying his petition for a writ of habeas corpus. The petitioner claims that the court abused its discretion by denying his petition for certification to appeal, and by rejecting his claims that (1) the state violated his rights to due process and a fair trial by failing to disclose material exculpable evidence and failing to correct false testimony from certain witnesses at his criminal trial, and (2) his criminal trial counsel rendered ineffective assistance. We conclude that the habeas court did not abuse its discretion in denying the petition for certification to appeal and, therefore, dismiss the appeal.
This case involves a homicide in New London. As the Supreme Court recounted in the petitioner's direct appeal, "James 'Tiny' Smith and Darrell Wattley fought at a party on July 4, 1995. Wattley sliced *798Smith's throat with a box cutter, wounding him superficially. On the afternoon of July 13, 1995, [the petitioner] and [Jamie] Gomez picked Smith up at the house of Smith's mother, and drove him to [Anthony] Booth's apartment at 93 State Pier Road in New London. When the three men arrived at Booth's apartment, Booth told them that he had asked Angeline Valentin, who lived in the same building, to call Wattley over to the building so that Wattley and Smith could fight. Booth, [the petitioner], Gomez and Smith watched television while they waited for Wattley to arrive. During their wait, and while [the petitioner] was rummaging through a grey knapsack, Booth asked [the petitioner] whether he '[had worn] gloves when he loaded it.' Booth also had a knife in his hand. When Smith asked Booth why he needed the knife, Booth replied: '[D]on't worry about it, we are just going to fight him.' *361"When Valentin called to say that Wattley was on his way, the four men left the building and went outside. Gomez and [the petitioner] went to the north side of the building while Smith and Booth went to the south side and hid behind a bush. While they were waiting, Booth was talking on a cellular telephone to either [the petitioner] or Gomez. After approximately fifteen minutes, a car arrived and Wattley got out. Wattley walked toward the north end of the building, where [the petitioner] and Gomez were waiting. Smith and Booth then entered the building on the south side and began to ascend the stairs. When Smith and Booth reached the third floor, where Valentin's apartment was located, they heard gunshots below. Smith and Booth then ran to exit the building. As they descended the stairs, they saw Wattley lying face down in the second floor hallway with blood everywhere. Booth then stabbed Wattley a couple of times before Smith and Booth fled the building.
"The four men ran to a red Mitsubishi, which was parked on State Pier Road, east of the building. This car was owned by Gomez' girlfriend, Dawn Waterson. Gomez sat in the driver's seat, and [the petitioner], Smith and Booth sat in the passenger seats. As they drove away, [the petitioner] said 'I robbed that nigger too.' [The petitioner] had a knife in his lap, which he threw out of the window while they were driving. Gomez drove Waterson's car across town and parked it behind a mall. The four men walked through a cemetery before splitting up. In the cemetery, Booth told them that, if questioned, he and [the petitioner] would say that they had been together. In addition, Booth told Smith and Gomez to come up with an alibi. The four men then separated.
"A few hours after the murder, Booth approached Valentin in the parking lot of 93 State Pier Road. Booth told her that they shot 'him.' Booth also told Valentin *362that he knew that she would not have lured Wattley to the building if she had known that they intended to murder him." (Footnote omitted.) State v. Booth , 250 Conn. 611, 614-15, 737 A.2d 404 (1999), cert. denied sub nom. Brown v. Connecticut , 529 U.S. 1060, 120 S.Ct. 1568, 146 L.Ed.2d 471 (2000).
The petitioner subsequently was arrested and a consolidated trial with Booth and Gomez followed, at the conclusion of which the jury found all three defendants guilty of murder in violation of General Statutes § 53a-54a, and conspiracy to commit murder in violation of General Statutes §§ 53a-54a and 53a-48 (a).2 Id., at 613, 737 A.2d 404. The petitioner directly appealed *799from that judgment of conviction, which our Supreme Court affirmed in a consolidated appeal with Booth and Gomez. Id., at 663, 737 A.2d 404.
The petitioner commenced this habeas action in 2013. On March 15, 2016, he filed a second amended petition for a writ of habeas corpus that contained two counts. The first alleged ineffective assistance on the part of his criminal trial counsel, Attorney Jeremiah Donovan, in failing to adequately cross-examine and impeach the testimony of Smith and Valentin.3 In the second count, the petitioner alleged a due process violation stemming from the state's handling of allegedly exculpatory evidence regarding the testimony of Smith and Valentin. More specifically, the petitioner alleged that the state "failed to disclose material favorable evidence to the petitioner with respect to an express or implied agreement" with both Smith and Valentin "for favorable treatment in [their] then pending criminal case[s] and *363failed to correct [their] false or misleading testimony concerning the same ...."
A habeas trial was held on March 5, 2016, at which Donovan was the sole witness.4 In its subsequent memorandum of decision, the habeas court rejected the petitioner's claims. With respect to his ineffective assistance of counsel claim, the court concluded that the petitioner failed to satisfy the prejudice prong of Strickland v. Washington , 466 U.S. 668, 686, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). As to his claims regarding the suppression of allegedly exculpatory evidence, the court found that the petitioner failed to prove the existence of an agreement between the state and Smith and Valentin that the state had suppressed. In so doing, the court acknowledged that Donovan, in his habeas testimony, confirmed that the state had assured Smith and Valentin that their "cooperation [at the petitioner's criminal trial] would be taken into consideration upon sentencing." The court nonetheless found that the petitioner had not met his burden in demonstrating that the state suppressed evidence of that assurance. The court further found that "even if the [state] had suppressed evidence, the petitioner also failed to prove that this evidence would have been material." The court, therefore, denied the petition for a writ of habeas corpus. The petitioner then filed a petition for certification to appeal to this court, which the habeas court denied, and this appeal followed.
On appeal, the petitioner claims that the court abused its discretion in denying the petition for certification to appeal. Our standard of review for such claims is *364well established. "Faced with a habeas court's denial of a petition for certification to appeal, a petitioner can obtain appellate review of the dismissal of his petition for habeas corpus only by satisfying the two-pronged test enunciated by our Supreme Court in Simms v. Warden , 229 Conn. 178, 640 A.2d 601 (1994), and adopted in Simms v. Warden , 230 Conn. 608, 612, 646 A.2d 126 (1994). First, [the petitioner] must demonstrate that the denial of his petition for certification constituted *800an abuse of discretion.... Second, if the petitioner can show an abuse of discretion, he must then prove that the decision of the habeas court should be reversed on the merits.... A petitioner may establish an abuse of discretion by demonstrating that the issues are debatable among jurists of reason ... [the] court could resolve the issues [in a different manner] ... or ... the questions are adequate to deserve encouragement to proceed further.... In determining whether the habeas court abused its discretion in denying the petitioner's request for certification, we necessarily must consider the merits of the petitioner's underlying claims to determine whether the habeas court reasonably determined that the petitioner's appeal was frivolous." (Citation omitted; internal quotation marks omitted.) Ramos v. Commissioner of Correction , 172 Conn. App. 282, 294, 159 A.3d 1174, cert. denied, 327 Conn. 904, 170 A.3d 1 (2017). With that standard in mind, we turn to the substantive claims raised by the petitioner.
I
The petitioner first contends that the court abused its discretion in denying his petition for certification to appeal because the state violated his right to due process and a fair trial by failing to disclose material exculpatory evidence in contravention of Brady v. Maryland , 373 U.S. 83, 87, 83 S.Ct. 1194, 10 L.Ed. 2d 215 (1963). The petitioner claims that the state suppressed evidence *365of an agreement between the state and Smith and Valentin in exchange for their testimony at the petitioner's criminal trial.
"The law governing the state's obligation to disclose exculpatory evidence to defendants in criminal cases is well established. The defendant has a right to the disclosure of exculpatory evidence under the due process clauses of both the United States constitution and the Connecticut constitution.... In order to prove a Brady violation, the defendant must show: (1) that the prosecution suppressed evidence after a request by the defense; (2) that the evidence was favorable to the defense; and (3) that the evidence was material....
"It is well established that [i]mpeachment evidence as well as exculpatory evidence [fall] within Brady 's definition of evidence favorable to an accused.... [An express or implied] plea agreement between the state and a key witness is impeachment evidence falling within the definition of exculpatory evidence contained in Brady ....
"The [United States] Supreme Court established a framework for the application of Brady to witness plea agreements in Napue v. Illinois , 360 U.S. 264, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959), and Giglio v. United States , 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972).... Drawing from these cases, [the Connecticut Supreme Court] has stated: [D]ue process is ... offended if the state, although not soliciting false evidence, allows it to go uncorrected when it appears.... If a government witness falsely denies having struck a bargain with the state, or substantially mischaracterizes the nature of the inducement, the state is obliged to correct the misconception.... Regardless of the lack of intent to lie on the part of the witness, Giglio and Napue require that the prosecutor apprise the court when he knows that his witness is giving testimony that *366is substantially misleading.... A new trial is required if the false testimony could ... in any reasonable likelihood have affected the judgment of the jury." (Citations omitted; internal quotation marks omitted.) State v. Ouellette , 295 Conn. 173, 185-86, 989 A.2d 1048 (2010). *801As our Supreme Court has explained, "[t]he prerequisite of any claim under the Brady , Napue and Giglio line of cases is the existence of an undisclosed agreement or understanding between the cooperating witness and the state." Id., at 186, 989 A.2d 1048. In its memorandum of decision, the habeas court found that no specific agreement existed between the state and either Smith or Valentin, apart from the state's assurance that it would bring their cooperation to the attention of the court in their respective criminal proceedings.
The petitioner now challenges the propriety of that determination. His claim is governed by the clearly erroneous standard of review. "The existence of an undisclosed plea agreement is an issue of fact for the determination of the trial court.... [W]here the factual basis of the court's decision is challenged we must determine whether the facts set out in the memorandum of decision are supported by the evidence or whether, in light of the evidence and the pleadings in the whole record, those facts are clearly erroneous." (Citations omitted; internal quotation marks omitted.) State v. Floyd , 253 Conn. 700, 737, 756 A.2d 799 (2000). "[A] finding of fact is clearly erroneous when there is no evidence in the record to support it ... or when although there is evidence to support it, the reviewing court on the entire evidence is left with the definite and firm conviction that a mistake has been committed." (Internal quotation marks omitted.) Orcutt v. Commissioner of Correction , 284 Conn. 724, 742, 937 A.2d 656 (2007). In reviewing the factual findings of a habeas court, "[t]his court does not retry the case or evaluate the credibility of the witnesses.... Rather, we must *367defer to the [court's] assessment of the credibility of the witnesses based on its firsthand observation of their conduct, demeanor and attitude.... The habeas judge, as the trier of facts, is the sole arbiter of the credibility of witnesses and the weight to be given to their testimony." (Internal quotation marks omitted.) Elsey v. Commissioner of Correction , 126 Conn. App. 144, 153, 10 A.3d 578, cert. denied, 300 Conn. 922, 14 A.3d 1007 (2011).
In this habeas proceeding, the petitioner bore the burden "to prove the existence of undisclosed exculpatory evidence." State v. Floyd , supra, 253 Conn. at 737, 756 A.2d 799. We agree with the habeas court that the petitioner did not satisfy that burden.
A
In its memorandum of decision, the court found that the state had assured both Smith and Valentin that it would bring their cooperation in the petitioner's criminal trial to the attention of the court in their respective criminal proceedings. The court further found that the state disclosed that agreement to the petitioner prior to his criminal trial.
The evidence in the record substantiates those findings. Donovan testified at the habeas trial that, in multiple conversations with the prosecutor, he was apprised that the state made "no promises to [Smith and Valentin] other than to bring their cooperation to the attention of the sentencing judge" in their respective proceedings. On the basis of his extensive experience dealing with the New London County Office of the State's Attorney, Donovan explained that the state's agreement to bring Smith's and Valentin's cooperation to the court's attention, but not make any specific promises or representations, was consistent with its general practice at that time. Donovan further confirmed that he was aware of that agreement prior to the petitioner's criminal trial.
*368The court, as the sole arbiter of credibility, was free to credit that testimony. See *802Sanchez v. Commissioner of Correction , 314 Conn. 585, 604, 103 A.3d 954 (2014) ("we must defer to the [trier of fact's] assessment of the credibility of the witnesses based on its firsthand observation of their conduct, demeanor and attitude" [internal quotation marks omitted] ); Taylor v. Commissioner of Correction , 284 Conn. 433, 448, 936 A.2d 611 (2007) ("[t]he habeas judge, as the trier of facts, is the sole arbiter of the credibility of witnesses and the weight to be given to their testimony" [internal quotation marks omitted] ). Moreover, at the conclusion of the habeas trial, the petitioner's counsel conceded that "[w]ith respect to the evidence that was introduced, [Donovan] was made aware that [Smith and Valentin's] cooperation would be brought to the sentencing judge's attention."
On the basis of that evidence, the court properly could find that the state disclosed to the petitioner its agreement with Smith and Valentin to bring their cooperation to the attention of the court in their respective criminal proceedings. That finding, therefore, is not clearly erroneous.
B
The petitioner nevertheless claims that, beyond the agreement addressed in part I A of this opinion, a specific agreement existed between the state and both Smith and Valentin regarding the lowering of their respective bonds, which was not disclosed to the petitioner.5 Under Connecticut law, the petitioner bore the burden of proving the existence of that agreement.
*369Walker v. Commissioner of Correction , 103 Conn. App. 485, 493, 930 A.2d 65, cert. denied, 284 Conn. 940, 937 A.2d 698 (2007).
The following additional facts, as reflected in the record and as recited in this court's recent decision on the habeas action involving one of the petitioner's coconspirators,6 are relevant to this claim. "On September 13, 1995, Valentin testified during a probable cause hearing for Booth that implicated Booth in Wattley's murder. During Valentin's bond hearing on October 5, 1995, Bernard Steadman, her attorney, represented: 'I have discussed this matter with the state and they would-my understanding is that there would be no objection to her moving out of state, should she be released on a bond, and provided that she maintain contact with-to or with their office either through me or directly.' Steadman asked the court to consider releasing Valentin on a promise to appear and allowing her to travel to New Jersey, given her cooperation with the state, and because Wattley's murder appeared to be gang related.7 Paul E. Murray, the supervisory assistant state's attorney (prosecutor),8 *803informed the court: 'I did indicate to [Steadman], Your Honor, that I would bring to the court's attention [Valentin's] cooperation, and I think I've done that.' The prosecutor also informed the *370court that he had spoken with Valentin's mother about Valentin going to New Jersey and that 'both [Valentin] and her mother have agreed ... to keep the state apprised as to her location and how she can be reached ....' In the event that she did not keep the state apprised of her location, the prosecutor stated that '[the state] will find her and she will have forfeited whatever benefits she has gained from her cooperation to this point.' He also stated: 'I'm not sure whether a promise to appear is the appropriate thing, but I think certainly a substantial reduction in her bond is appropriate.' Thereafter, the prosecutor stated that he would not object to a written promise to appear and informed the court: 'I think if I were in your position, I would not be averse to a written promise to appear. I'm trying to be careful as to-as to the record I'm making.'
"After considering, inter alia, the 'cooperative aspects of this matter,' the court, Purtill, J ., reduced Valentin's bond from $100,000 to a written promise to appear and permitted her to reside in New Jersey. Immediately following that decision, the following colloquy took place in open court:
" '[The Prosecutor]: ... For the record, I would indicate I do not disagree at all with the court's decision. I was trying to be careful with the record because of obvious cross-examination effect. In consideration, I want the record to be clear that the only representations made to [Valentin ] were that any cooperation would be brought to the attention of the sentencing court. There was no quid pro quo for a specific bond recommendation .
" '[Steadman]: That is true, Your Honor.' ...
"On March 14, 1996, during a consolidated probable cause hearing for [the petitioner and Gomez], Smith provided testimony that implicated [them] in Wattley's murder. [Gomez and his trial counsel] attended this *371hearing, and so did Donovan, [the petitioner's] lawyer. At the beginning of Smith's testimony, the following examination took place in open court:
" '[The Prosecutor]: And you are in fact charged with murder, felony murder, and conspiracy to commit murder with respect to the case that we are going to talk about, is that right?
" '[Smith]: Yes.
" '[The Prosecutor]: And is it fair to say that other than bringing your cooperation to the attention of the sentencing court , you haven't been promised anything in return for your testimony?
" '[Smith]: No.
" '[The Prosecutor]: You say 'no.' That is the truth, isn't it?
" '[Smith]: That's the truth.' ...
"On May 3, 1996, approximately two months after Smith testified at the consolidated probable cause hearing, the court, Parker, J ., addressed Smith's motion for modification of his bond. The state did not object to the motion. Counsel for Smith represented that the reasons for requesting a bond modification were that Smith's life had been threatened and he had cooperated with the state. Thereafter, the court reduced Smith's bond from $500,000 to *804$100,000 and permitted him to travel throughout the continental United States.
"On May 10, 1996, the court, Purtill, J ., amended the terms of Smith's bond, making it a $100,000 nonsurety bond with a nominal real estate bond. During this hearing, the prosecutor stated that the state had been in *372contact with a parole officer in Alabama, who agreed to arrange weekly reporting with Smith if he were allowed to reside there. The court asked that the state 'reduce that condition to writing and give a copy to ... Smith.' Smith was then permitted to be released on bond." (Emphasis in original; footnotes added and footnote in original.) Gomez v. Commissioner of Correction , 178 Conn. App. 519, 529-31, 176 A.3d 559 (2017).
On appeal, the petitioner renews his claim that a specific agreement existed between the state and Smith and Valentin regarding the lowering of their respective bonds. He presented the habeas court with no evidence of such a specific agreement. The petitioner did not call Smith, Valentin, or their trial attorneys as witnesses at the habeas trial, nor did he introduce the testimony of the prosecutor. The only evidence he submitted to support his claim was the transcripts of the bond hearings, which merely indicate that the state did not object to the bond reductions contemplated therein. The transcripts also contain statements regarding the specific rationales for those bond reductions. In Smith's case, it was the undisputed fact that "his life [had] been threatened" while incarcerated. In Valentin's case, it was because she was only sixteen years old, had no criminal record at the time of the July 13, 1995 homicide, and her family was planning on moving out of state due to "the gang involvement" in that homicide. See footnote 7 of this opinion. In granting the requested bond reduction, the court, Purtill, J ., stated that it was "considering mainly the youth of this young lady and the fact that she would have to be-if she was kept in confinement here, it would have to be in segregation because of the circumstances; and for a person of her age it probably is not at all appropriate, as mentioned by counsel. That's the main reason the bond is being reduced."
*373Furthermore, those bond hearing transcripts do not indicate that any agreement existed between the state and Smith and Valentin, apart from the assurance that their cooperation in the petitioner's criminal proceeding would be brought to the sentencing judge's attention. As the prosecutor expressly stated during Valentin's October 5, 1995 bond hearing: "I want the record to be clear that the only representations made to [Valentin] were that any cooperation would be brought to the attention of the sentencing court. There was no quid pro quo for a specific bond recommendation." In response, Valentin's attorney stated, "That is true, Your Honor."9
That testimony is consistent with that offered by Donovan at the petitioner's habeas trial. Donovan testified that, as a matter of practice, the New London County Office of the State's Attorney would not make "any specific promises" apart from the assurance that the cooperation of such witnesses would be brought to the attention of the court in their own criminal proceedings.
Our review of the record reveals that the petitioner did not present evidence at his habeas trial that compelled a finding that the state reached an agreement with *805Smith and Valentin to give favorable treatment at their bond hearings in exchange for their testimony at the petitioner's criminal trial. In light of the foregoing, the court properly concluded that the petitioner had not met his burden in demonstrating the existence of a specific agreement between the state and Smith and Valentin regarding their bond proceedings. Absent such an agreement, the petitioner's Brady claim, as well as his related claim that the state failed to correct false testimony related thereto, necessarily fails. See State v. Ouellette , supra, 295 Conn. at 186, 989 A.2d 1048.
II
*374The petitioner also claims that the court abused its discretion in denying his petition for certification to appeal because Donovan rendered ineffective assistance by failing to adequately cross-examine and impeach the testimony of Smith and Valentin at trial. That claim is premised on the undisputed fact that Donovan did not order, and thus did not review and utilize, the transcripts of Smith and Valentin's bond hearings.
"To succeed on a claim of ineffective assistance of counsel, a habeas petitioner must satisfy the two-pronged test articulated in Strickland v. Washington , [supra, 466 U.S. at 668, 104 S.Ct. 2052 ]. Strickland requires that a petitioner satisfy both a performance prong and a prejudice prong. To satisfy the performance prong, a claimant must demonstrate that counsel made errors so serious that counsel was not functioning as the counsel guaranteed ... by the [s]ixth [a]mendment.... To satisfy the prejudice prong, a claimant must demonstrate that there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different.... Although a petitioner can succeed only if he satisfies both prongs, a reviewing court can find against a petitioner on either ground." (Citations omitted; internal quotation marks omitted.) Breton v. Commissioner of Correction , 325 Conn. 640, 668-69, 159 A.3d 1112 (2017).
Although he did not obtain the transcripts of their bond hearings, Donovan testified that, at the time of the petitioner's trial, he was aware that Smith and Valentin "had been released on bond." Donovan testified that he knew why their bonds had been reduced, which he utilized in his cross-examination of those witnesses at trial. The transcripts of the petitioner's trial, which were admitted into evidence at the habeas trial, demonstrate *375that Donovan questioned both Smith10 and Valentin11 *806extensively on the issue of their bond reductions, and *376the motivations therefor, during the petitioner's criminal trial. Furthermore, as the habeas court noted in its memorandum of decision, the transcripts reveal "that counsel for the petitioner's codefendants also questioned both Valentin and Smith concerning their bond reductions. During [their] cross-examination of Valentin, they both questioned her regarding the fact that her $150,000 bond was reduced to a promise to appear after she testified at a preliminary hearing. Furthermore, [Booth's attorney] questioned Smith regarding the fact that his $500,000 bond was reduced and he was subsequently released after he testified at the probable cause hearing." In addition, both Smith and Valentin in their testimony at the petitioner's trial admitted that they hoped that their cooperation would be taken into account with regard to their pending charges. *377We also note that, in their closing remarks to the jury, Donovan and counsel for the petitioner's codefendants all reminded jurors of the circumstances surrounding the bond reductions for Smith and Valentin, and suggested that those reductions were connected to their testimony in the consolidated trial. They thus encouraged the jury to consider that connection in assessing their credibility as *807witnesses. Additionally, in its charge to the jury, the court provided an accomplice testimony instruction, which cautioned jurors that the testimony of an accomplice could be "colored" by the fact that such witnesses may "be looking for or hoping for some favorable treatment in the sentence or disposition of his or her case ...."12 Absent an indication to the contrary, the jury is presumed to have heeded that instruction. See State v. Wooten , 227 Conn. 677, 694, 631 A.2d 271 (1993) ("[j]urors are presumed to follow the instructions given by the judge" [internal quotation marks omitted] ).
The record before the habeas court thus demonstrates that the reduction of Smith's and Valentin's bonds, as well as Smith's and Valentin's incentive to testify at the petitioner's trial, repeatedly was brought to the attention of the jury at the petitioner's trial. The petitioner has not demonstrated how Donovan's failure to obtain the transcripts of the bond proceedings *378resulted in prejudice, apart from asserting that a review of those transcripts would have enabled him to impeach Smith's and Valentin's allegedly false testimony that there was no specific agreement between them and the state regarding those bond proceedings. That assertion fails in light of the habeas court's determination that no such agreement had been proven, and thus no Brady violation transpired, which determinations we have affirmed in part I of this opinion. On our thorough review of the record, we conclude that the habeas court properly determined that the petitioner has not demonstrated a reasonable probability that, but for Donovan's alleged failure to obtain the bond hearing transcripts and cross-examine Smith and Valentin therewith, the result of the petitioner's criminal trial would have been different. Accordingly, we conclude that the habeas court did not abuse its discretion in denying the petition for certification to appeal.
The appeal is dismissed.
In this opinion the other judges concurred.